The former US secretary of state said she believes a yes vote would be a "loss for both sides" and she is hoping that it does not happen.
Mrs Clinton, who is on a tour to promote her memoir Hard Choices and is widely believed to be preparing for a presidential run in 2016, also indicated she was keen for Britain to remain part of the European Union.
"I would hate to have you lose Scotland," she told BBC Newsnight.
"I hope that it doesn't happen but I don't have a vote in Scotland. But I would hope it doesn't happen."
She added: "I would think it would be a loss for both sides but, again, I don't have a vote."
Mrs Clinton insisted the so-called special relationship between Britain and the US was "worth everything to me and to our country".
"I do think we see the world very similarly," she added.
Asked if Britain's standing would be enhanced or diminished in the United States if it left the European Union, she replied: "Oh, boy you are asking me to cross into dangerous waters, which I will not do."
She added: "Europe needs Britain, in my opinion. I think Britain brings a perspective and an experience that is very important to Europe, especially post-economic crisis.
"So, Britain will have to decide if they agree with that."
Mrs Clinton's intervention in the referendum debate comes just one week after US president Barack Obama said he believed that the United Kingdom appears to have "worked pretty well".
A spokesman for Yes Scotland said of Mrs Clinton's comments: "As she says, the decision about Scotland's future is one for the people of Scotland to make. After a Yes vote, the friendship between Scotland and the United States will flourish to the benefit of both nations."
A Better Together spokesman said: "Hillary Clinton is a figure who is respected right across the world. Like President Obama, she understands that the UK is at its strongest when it works together.
"She has said 'no thanks' to Alex Salmond's attempts to divide the people of Britain. We are grateful for her support."
Shadow foreign secretary Douglas Alexander welcomed Mrs Clinton's comments, which follow those of Mr Obama and come the day after Harry Potter author JK Rowling made a £1 million donation to the No campaign.
Asked whether such outside interventions could rile people, he told BBC Radio Scotland: "If you would like to argue that President Barack Obama, JK Rowling and now Hillary Clinton are a problem for the No campaign, good luck. These are all, independently, figures who are hugely admired here in Scotland and I think you would be hard -pressed to find a female politician anywhere in the world that is admired as much by Scottish women as Hillary Clinton.
"I don't think this is an inadvertent slip of the tongue, this is a woman who as America's senior diplomat over the last four years has chosen her words extraordinarily carefully and I think it's very significant that she's expressed, certainly the fact that it's for those of us in Scotland to make the choice, but a very clear personal view that she would hate it and thinks that it would be better for us to stay together.
"Hillary Clinton has travelled the world for four years as secretary of state, she knows and understands that there are many provinces in China that are larger than any one country within the European Union, even Germany the most populous country within the European Union, and I think she has that broader view that recognises that the hallmark and the challenge of this time is not so much independence as interdependence, h. How do we establish networks of co-operation to meet common challenges from giving global economic growth in a sustainable way to tackling climate change?
"And in that sense I think that global view, that broader perspective, gives her a sense as to what would not just be in Scotland's interest or in the rest of the United Kingdom's interest but more broadly in European and Western interests as well, that we're able to continue to pull together and work together in the face of some big common challenges that we face."
Scottish First Minister Alex Salmond said: "Hillary Clinton is of course entitled to her views and, as she rightly points out, the referendum is a matter for the people of Scotland.
"Mrs Clinton's observations are quite interesting in that she infers Britain will 'lose Scotland' after a Yes vote.
"This reflects reports that David Cameron has said he doesn't want to 'lose' Scotland, likening it to George III losing the United States.
"But, unlike that period in American history - when independence was only gained through conflict - we are deeply fortunate in that we have the opportunity to secure our nation's independence in a profoundly democratic way, as president Obama and John Kerry, Mrs Clinton's successor as Secretary of State, have acknowledged."
Mr Salmond continued: "In any case, Scotland is not a property to be lost but a nation about to take a precious and consensual and democratic decision.
"An independent Scotland will be a friend and ally to our neighbours in the rest of the UK as well as to our friends in the United States of America.
"The eyes of the world are on Scotland as we look forward to one of the most exciting days in our history - but that huge international focus, and all the economic and other opportunities it will bring, will only stay on Scotland with a Yes vote."