A judge convicted and sentenced Mohammad Asghar, from Edinburgh, on Thursday following a trial.
Mr Asghar was arrested in 2010 in Rawalpindi, near the capital Islamabad, for claiming to be the Prophet Mohammed in letters sent to various officials, according to prosecutor Javed Gul.
But a lawyer who defended Mr Asghar said he suffers from mental illness and the case was really a property dispute.
Amnesty International's deputy Asia Pacific director Polly Truscott said: "Mohammad Asghar is now facing the gallows simply for writing a series of letters. He does not deserve punishment. No one should be charged on the basis of this sort of conduct.
"The blasphemy laws undermine the rule of law, and people facing charges risk death and other harm in detention.
"Pakistan must immediately release Mohammad Ashgar and reform its blasphemy laws to ensure that this will not happen again."
Mr Asghar, a UK citizen of Pakistani origin, returned to Pakistan in 2010 after being treated for paranoid schizophrenia in Edinburgh, the lawyer said.
He later fell into a dispute with a tenant who brought the blasphemy complaint against him to police.
A doctor treating Mr Asghar in Edinburgh said in a letter dated June 2011 that he suffered from paranoid schizophrenia and believed that the Pakistani and British governments were attempting to control him.
The letter was provided to The Associated Press by his lawyer, who asked not to be named for fear of threats and violence.
Prosecutors disputed that Mr Ashgar had mental problems.
The British High Commission in Islamabad said it was aware of Mr Asghar's case and provided assistance to him.
Lawyers said they will appeal against the conviction, and that they are worried about his mental condition and physical safety in prison.
Another British citizen, Masud Ahmad, of the Ahmadi sect, was imprisoned in November 2012 for reciting a passage from the Koran, a prohibited act for Ahmadis under the country's blasphemy laws.
Ms Truscott said: "The Pakistani authorities must immediately and unconditionally release both Mohammad Asghar and Masud Ahmad and guarantee their safety and that of their families. Several individuals have been attacked, some even killed following charges of blasphemy.
"At a time when Pakistan is reeling from a spate of abuses which perpetrators seek to justify as a defence of religious sentiments, reform of the blasphemy laws is more urgent than ever."
A Scottish Government spokesman said: "We're concerned about this case and can confirm that we have been in touch with the FCO who will keep us informed of the situation.
"The Scottish Government strongly opposes the death penalty in all circumstances. As a minimum we would urge the Pakistani authorities to abide by the moratorium they have on the death penalty.
"Our thoughts are with Mr Asghar's family at this difficult time."
Scores of people have been arrested in Pakistan under the country's harsh blasphemy laws, which carry sentences of life in prison or the death penalty, though executions are rarely carried out.
Rights groups say the laws often are exploited for personal gain and that members of Pakistan's minority population are disproportionately targeted.
People accused of blasphemy also have been attacked and killed by angry vigilante mobs.
Few leaders in the predominantly Muslim country have shown willingness to tackle the contentious issue, especially after two prominent politicians who criticised the blasphemy law were murdered in recent years.
One of the politicians was shot by his own bodyguard, who then attracted adoring crowds.