Abdul Rahman converted from Islam to Christianity 16 years ago while living abroad. He had been due to be tried for apostasy in Kabul and could have faced the death penalty.
The case has been referred back to the prosecutor-general, who has ordered an examination to determine Rahman's mental state.
Under local laws, if Afghan mental health experts judge Rahman to be insane, the charges against him could be dismissed.
The case has drawn international attention. The pope, who has called for Rahman's release, said on March 26 he is praying for all Christians facing hostility around the world.
"My thoughts turn particularly to those communities in countries where there is no religious freedom, or where, despite it being set out on paper, there are many restrictions," he said.