The militants were killed in the encounter at Awoora village in Pahalgam area of the district, an army official said.
Acting on specific intelligence input about the presence of militants in the village, security forces yesterday launched a search operation in the area.
As the forces were conducting the search operation, the hiding militants fired upon them, he said, adding the security forces retaliated, ensuing an encounter.
The exchange of fire went on till late in the evening after which it was halted for the night, the official said, adding it was resumed in the wee hours today and the three militants were killed in the gunfight.
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The slain militants were seen in a video which recently surfaced on social media showing them enjoying the snowfall in the Valley, Superintendent of Police, Anantnag, Zubair Ahmad told PTI.
"The three militants were part of the six militants in that video where they were playing in snow," he said.
The video showed the militants enjoying snowfall and brandishing AK 47 assault rifles while treading a snow-clad hillock after heavy snowfall on January 6.