A senior police officer said militants hurled a grenade at a paramilitary, Central Reserve Police Force camp near the town hall building in Sopore.
The grenade exploded near the entrance to the camp injuring a cop of the state police who was passing by. He was shifted to hospital
for treatment, the officer said.
The area was immediately surrounded for searches.
Militants hurled another grenade at the heavily guarded police station building in Sopore town, which exploded without causing any damage.
The explosions triggered panic and tension in the town on Tuesday evening.
No group has yet claimed responsibility for the twin blasts.