This is the second major attack against police in six weeks.
Mattoo had gained notoriety after he shot dead two policemen in broad daylight at the busy Anantnag bus stand in June 2016.
"Three militants were killed in gunfight at Aarwani village", Indian army spokesperson Col Rajesh Kalia said, "The bodies have been recovered this morning along with three assault rifles".
File image of deceased LeT commander Junaid Matoo.
Officials said clashes also broke out between protesters and security forces at almost a dozen places in the Valley, including Jamia Masjid in downtown Srinagar, Tral, Pampore, Pulwama town and Anantnag in south Kashmir, Hajin in Bandipora and Sopore in Baramulla in north Kashmir. Several people were reportedly injured.
"It is because of the stubborn and rigid approach of the New Delhi towards Kashmir and its people that killing of innocent civilian has become a daily feature". The Kashmir University postponed examinations scheduled for Saturday.
The cordon and search operation started at around 8am in Malik Mohalla of Arwani, area of Kulgam around 55 kms from Srinagar, which triggered a gun battle between forces and the militants.
Junaid Mattoo was one of the 12 most wanted terrorists in the valley.
Others who have been killed in the attack include constables Sharik Ahmad and Tanveer Ahmad (Budgam district), Sheraz Ahmad (Achabal), Asif Ahmad and Sabzar Ahmed (Anantnag).
20-year-old Mattoo, who has been listed as a "Category A" terrorist carried a bounty of Rs 10 lakh on his head.
Confirming the two deaths, DGP SP Vaid said: "Security forces have no choice but to retaliate when militants fire at them". Two civilians received bullet injuries but were reported to be out of danger.
Earlier on Thursday evening, another civilian Nazir Ahmad was killed in Rangreth area of Srinagar, when SSB personnel opened fire at protestors pelting stones.
The terrorists were eliminated after an encounter that lasted for hours.
Meanwhile, normal life in Valley was affected by the strike called by separatists and restrictions imposed by authorities to maintain law and order.