A "hybrid terrorist" from the banned local outfit Lashkar-e-Taiba (LeT) has been arrested for carrying out the attacks during a search and surveillance operation, they said.
"Hybrid terrorists" are unlisted fighters who carry out terrorist attacks and often return to their everyday lives without a trace.
Terrorists hurled a grenade in Shopian's Harmen area, injuring two labourers, Monish Kumar and Ram Sagar, both residents of Uttar Pradesh's Kannauj. They were shifted to the hospital, where they succumbed to their injuries, Kashmir Zone Police said in a tweet.
The area was cordoned off and a hunt was launched to nab the attackers, it said.
During the operation, a hybrid terrorist of LeT, who lobbed the grenade, was arrested, said Kashmir Police in a Twitter post.
The arrested terrorist was identified as Imran Bashir Ganie from Harmen, he said.
Further investigation and raids are underway, the ADGP said.
This came two days after a Kashmiri Pandit was shot down. On Saturday, militants killed Bhat, a 48-year old Kashmiri Hindu in Chowdhry Gund village of the district.
Attacks have increased since October when militants attacked Kashmiri pandits and workers outside the valley in a series of attacks.
According to official documents, four Kashmiri Pandits have been killed in terrorist attacks this year.
Militants also carried out several similar attacks on minorities of Kashmir and non-local workers in May.
With inputs from agencies
