The civilians were killed allegedly in firing by the security forces during clashes with stone-pelting protesters in Kulgam today, they said.
Mobile internet has been suspended in the entire Kashmir Valley, a police official said.
He, however, said broadband services on BSNL landlines were working.
The decision to suspend the mobile internet services is a precautionary measure to maintain law and order, he said.
Authorities also imposed restrictions in some parts of Kashmir today, while security was beefed up across the Valley on the eve of Hizbul Mujahideen commander Burhan Wani's second death anniversary.
Wani, a resident of Tral, was killed in an encounter with security forces in Kokernag area of south Kashmir's Anantnag district on July 8, 2016.
His killing had triggered massive protests and prolonged period of curfews and shutdowns across the Valley.