Lady Warsi, who was the first Muslim to sit in Cabinet, informed Prime Minister David Cameron that she could no longer support the Government's stance on the issue.
She wrote in her resignation letter: "My view has been that our policy in relation to the Middle East peace process generally but more recently our approach and language during the current crisis in Gaza is morally indefensible, is not in Britain's national interest and will have a long-term detrimental impact on our reputation internationally and domestically."
Lady Warsi's resignation appeared to have caught No 10 by surprise, with Mr Cameron currently out of the country on holiday.
It comes amid growing unease among some Conservative MPs that the Government has failed to take a firmer line with Israel over its incursion into Gaza in the face of mounting Palestinian casualties.
Lady Warsi has signalled her own concern about what was happening in a series of comments on her Twitter feed in recent days.
In one she wrote: "Can people stop trying to justify the killing of children. Whatever our politics there can never be justification, surely only regret #Gaza."
In another just three days ago she said: "If there is a community meeting or protest in relation to Gaza happening near you I'd like to know, please tweet me the details."
Speaking to the Huffington Post UK website following her resignation, Lady Warsi said the UK had forfeited its role as an honest broker in the region and called for an immediate arms embargo on Israel.
"The British Government can only play a constructive role in solving the Middle East crisis if it is an honest broker and at the moment I do not think it is," she said.
Reacting to the news, Deputy Prime Minister Nick Clegg said: "The Prime Minister must speak for himself. He's been clear that he regards the violence in Gaza as appalling and has called repeatedly for a humanitarian ceasefire.
"As for the correspondence between him and Sayeeda Warsi, this is the first I've heard about it and it's entirely, of course, a decision for the Prime Minister."
He added: "The Government's position has been, has argued consistently in favour of peace rather than conflict and ceasefire rather than violence. We've done that at all levels, regardless of what party we're from in the coalition.
"There are differences of emphasis, longstanding differences of emphasis about how forceful the Government should be, and how forceful Britain should be in seeking to bring the two sides together.
"As you know, I've come to the view, unpalatable though I totally understand it must seem to people perhaps on both sides of the conflict, I see no short cut but in the long run for some kind of negotiation between Hamas, or the political leadership in Gaza and Israel."
Mr Clegg called for a greater role for the EU, saying it was an economic giant in the region which "acts like a political pygmy".
He said: "This is one of those heartrending issues that inflames passions and divides opinions and always has done and I suspect always will."
For Labour, shadow foreign secretary Douglas Alexander said many people would support her reasons for resigning.
"Most reasonably-minded people across Britain will agree with the sentiments expressed by Baroness Warsi in her resignation statement today," he said.
"It is a sad reflection of the Prime Minister's misjudgment of the crisis in Gaza that this capable minister has felt the need to leave the Government.
"Labour has consistently opposed the Israeli incursion into Gaza and has repeatedly urged the Prime Minister to speak up and to speak out against the horrific loss of life witnessed in recent weeks, but he has so far failed to do so."
In her resignation letter, posted on her Twitter page, Lady Warsi expressed concern at the impact of changes in last month's Cabinet reshuffle on Government policy.
She pointedly described William Hague, who was moved from the Foreign Office, as "one of the finest foreign secretaries this country has seen", before adding: "There is, however, great unease across the Foreign Office, amongst both ministers and senior officials, in the way recent decisions have been made."
She also highlighted the departures of Cabinet veteran Ken Clarke and Dominic Grieve, the former attorney general, both seen as strong upholders of international law.
She pointed to evidence emerging from the Home Office suggesting the fallout from the conflict in Gaza and Britain's response to it would be a basis for radicalisation which "could have consequences for us for years to come".
Lady Warsi became the first Muslim to sit in the Cabinet when she was made Conservative Party co-chairman by David Cameron following the 2010 general election.
She was subsequently moved to the post of minister of state at the Foreign Office and minister for faith and communities in Mr Cameron's 2012 reshuffle in a move widely regarded as a demotion.
Her departure will be a blow to the Prime Minister - both because of the way that it highlights divisions within the Tory ranks over Middle East policy and because it marks the loss of a woman minister at a time when he has been trying to promote more women in Government.
London mayor Boris Johnson paid tribute to her, saying he hoped she would make a return to the Government soon.
"I have very great respect for Sayeeda. She has done a great job for us and I hope she will be back as soon as possible," he said during an LBC radio phone-in.
While Mr Johnson, who described himself as a "passionate Zionist", said that politicians across the political spectrum were horrified at what had been happening in Gaza, he went on to condemn the Israeli action as "disproportionate" - a word Mr Cameron and Foreign Secretary Philip Hammond have consistently avoided.
"I can't for the life of me see how this can be a sensible strategy," he said. "I think it is disproportionate, I think it is ugly and it is tragic and I don't think it will do Israel any good in the long run."
A Downing Street spokesman said: "The Prime Minister regrets that Baroness Warsi has decided to stand down and is grateful for the excellent work that she has done, both as a minister and in opposition.
"Our policy has always been consistently clear - the situation in Gaza is intolerable and we've urged both sides to agree to an immediate and unconditional ceasefire."
Here is the text of Baroness Warsi's letter of resignation in full:
Dear Prime Minister
For some weeks, in meetings and discussions, I have been open and honest about my views on the conflict in Gaza and our response to it.
My view has been that our policy in relation to the Middle East Peace Process generally but more recently our approach and language during the current crisis in Gaza is morally indefensible, is not in Britain's national interest and will have a long term detrimental impact on our reputation internationally and domestically.
Particularly as the Minister with responsibility for the United Nations, The International Criminal Court and Human Rights I believe our approach in relation to the current conflict is neither consistent with our values, specifically our commitment to the rule of law and our long history of support for International Justice. In many ways the absence of the experience and expertise of colleagues like Ken Clarke and Dominic Grieve has over the last few weeks become very apparent.
The decision has not been easy. It has been a privilege to serve for 3 years in your Shadow Cabinet and over 4 years in your Cabinet. Introducing you in Blackpool in 2005 as you made your bid for leadership I had the pleasure of being there at the start of the journey and it would have been rewarding to have been there till the end.
The last decade has given me the opportunity to work with some of the best in the Conservative Party and indeed in government. William Hague was probably one of the finest Foreign Secretaries this country has seen and has been inspirational. He dismantled foreign policy making by sofa government and restored decision making and dignity to the Foreign Office. There is however great unease across the Foreign Office amongst both Ministers and senior officials, in the way recent decisions are being made.
Eric Pickles has supported me tirelessly in our work on combating hate crime, challenging anti-Semitism and Islamaphobia and the pioneering work of celebrating faith in the public sphere. This new found confidence in Government has allowed me to take the very public international lead on religious freedom, specifically on the ever growing crisis of the persecution of Christians.
However, early evidence from the Home Office and others shows that the fallout of the current conflict and the potential for the crisis in Gaza and our response to it becoming a basis for radicalisation could have consequences for us for years to come.
From both Eric and William I learnt the art of reconciling passion and idealism with pragmatism and realism, but I always said that long after life in politics I must be able to live with myself for the decisions I took or the decisions I supported. By staying in Government at this time I do not feel I can be sure of that.
It is therefore with regret that I am writing to resign.
You will continue to have my personal support as leader of the Conservative Party as you continue to ensure that our Party evolves to meet the challenges we face in Britain today and ensure that the Party is relevant and responsive to all communities that make up today's Britiain.