The announcement came as U.S.-backed President Hamid Karzai faced mounting foreign pressure to free Abdul Rahman, a move that risked angering Muslim clerics who have called for him to be killed.
An official closely involved with the case told The Associated Press that it had been returned to the prosecutors for more investigation, but that in the meantime, Rahman would be released.
"The court dismissed today the case against Abdul Rahman for a lack of information and a lot of legal gaps in the case," the official said Sunday, speaking on condition of anonymity because he was not authorized to speak publicly on the matter.
"The decision about his release will be taken possibly tomorrow," the official added. "They don't have to keep him in jail while the attorney general is looking into the case."
CBS News consultant Jere Van Dyk said Rahman will still be in great danger when he is released. He said Rahman was moved from a jail in the city to a more secure prison.
If Islamists succeed in killing Rahman after his release, Van Dyk said "they will show again that Afghanistan is not in control of its own security, that it is totally dependent on the West and that the war between Islamists and the west will continue."
Abdul Wakil Omeri, a spokesman for the Supreme Court, confirmed that the case had been dismissed because of "problems with the prosecutors' evidence."
He said several family members of Rahman have testified that he has mental problems.
"It is the job of the attorney general's office to decide if he is mentally fit to stand trial," he told AP.
A Western diplomat, also declining to be identified because of the sensitivity of the case, said questions were being raised as to whether Rahman would stay in Afghanistan or go into exile in a foreign country.
Rahman is being prosecuted under Afghanistan's Islamic laws for converting 16 years ago while working as a medical aid worker for an international Christian group helping Afghan refugees in Pakistan.
"This is something that has been created by militant Islamists part in Afghanistan and Pakistan and elsewhere," Van Dyk said. "It's a way to further their power it's a way to embarrass a puppet government, that is to say Karzai."
Karzai's office has declined to comment on the case. Karzai is in a tough spot as pressure mounts from both the West to free Rahman and internally from Muslic clerics, who say they want Rahman dead.
On Saturday, Karzai searched for a way to free Rahman without angering Muslim clerics who have called for him to be killed.
"They will do everything they can to sweep it under the rug," Van Dyk said. "Many parts of Afghanistan particularly the rural areas, are deeply conservative they do not want anything like this to occur."
Karzai and several Cabinet ministers discussed Rahman's case, an official at Karzai's palace said. But she declined to comment on the outcome of the talks.
Hours earlier, another official said Rahman "could be released soon." Both spoke on condition of anonymity because they were not authorized to discuss the matter with the media.
Pope Benedict XVI has sent a message to Karzai asking that the case be dropped, citing respect for religious freedom, the Vatican said Saturday.