Abdul Rahman, 41, has been charged with rejecting Islam, a crime under this country's Islamic laws. His trial started last week and he confessed to becoming a Christian 16 years ago. If convicted, he could be executed.
But prosecutor Sarinwal Zamari said questions have been raised about his mental fitness.
"We think he could be mad. He is not a normal person. He doesn't talk like a normal person," he told The Associated Press.
Moayuddin Baluch, a religious adviser to President Hamid Karzai, said Rahman would undergo a psychological examination.
"Doctors must examine him," he said. "If he is mentally unfit, definitely Islam has no claim to punish him. He must be forgiven. The case must be dropped."
It was not immediately clear when he would be examined or when the trial would resume. Authorities have barred attempts by the AP to see Rahman and he is not believed to have a lawyer.
A Western diplomat in Kabul and a human rights advocate — both of whom spoke on condition of anonymity because of the sensitivity of the matter — said the government was desperately searching for a way to drop the case because of the reaction it has caused.
The United States, Britain and other countries that have troops in Afghanistan have voiced concern about Rahman's fate.
The Bush administration Tuesday issued a subdued appeal to Kabul to let Rahman practice his faith in safety.
German Roman Catholic Cardinal Karl Lehmann said the trial sent an "alarming signal" about freedom of worship in Afghanistan.
It has also received widespread attention in Afghanistan where many people are demanding Rahman be severely punished.
"For 30 years, we have fought religious wars in this country and there is no way we are going to allow an Afghan to insult us by becoming Christian," said Mohammed Jan, 38, who lives opposite Rahman's father, Abdul Manan. "This has brought so much shame."
Even the state-sponsored Afghanistan Independent Human Rights Commission has called for Rahman to be punished, claiming he clearly violated Islamic law.
Rahman is believed to have converted from Islam to Christianity while working as a medical aid worker for an international Christian group helping Afghan refugees in the Pakistani city of Peshawar.
He then moved to Germany for nine years before returning to Kabul in 2002, after the ouster of the hard-line Taliban regime.
Police arrested him last month after discovering him in possession of a Bible during questioning over a dispute for custody of his two daughters.
Afghanistan's constitution is based on Shariah law, which is interpreted by many Muslims to require that any Muslim who rejects Islam be sentenced to death.
Prosecutors have offered to drop the charges if Rahman converts back to Islam, but the defendant has refused.
The case is believed to be the first of its kind in Afghanistan and highlights a struggle between religious conservatives and reformists over what shape Islam should take there four years after the ouster of the Islamic fundamentalist Taliban regime.