The encounter in Panzgam village erupted after a joint team of police and army cordoned off the area to look for militants after receiving specific intelligence, an army official said.
As the forces were conducting a search operation, the hiding militants fired upon them, the official said.
In the ensuing gunfight, three militants -- all locals who belonged to Hizbul Mujhahdeen militant group -- were killed, he said.
Three weapons have also been recovered from the encounter site, he added.
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After the gunfight, a grenade lying there exploded, injuring a civilian who was among those who had assembled at the encounter site, a police official said.
The civilian, Wakeel Ahmed Shergujri, was taken to SKIMS Hospital in Srinagar where his condition is said to be stable.
When the news of the death of the three militants spread, some locals staged protests and pelted stones on security forces who fired teargas in retaliation, the official said.
"The train service has been suspended for today due to the prevailing law and order situation in Pulwama where from the trains pass towards Banihal," a Railway official said.
He said the decision was taken in view of apprehensions of protests in the area which may have lead to damage to railway property.