At least two other people were wounded in the attack, a police officer said on condition of anonymity as he was not authorized to talk to reporters. Srinagar is the main city in the Indian portion of Kashmir.
Police believe that the explosive was tied to a parked bicycle and triggered by a remote control, the officer said
The motive for the attack was not immediately known. No rebel group claimed responsibility for the killing.
"I heard the blast and immediately came out of the mosque to see him (Shah) lying in a pool of blood. There was a mangled bicycle nearby," said Sajad Ahmed, a local resident.
Since 1989, more than a dozen Islamic militant groups have been fighting for Kashmir's independence from India or its merger with neighboring Pakistan.