The terrorist was killed in the encounter near Trehgam town at 5.30 am, Defence Ministry spokesman Colonel Rajesh Kalia told IANS.
"It was a specific operation based on intelligence inputs and the operation is now over," Kalia added.
In a separate incident, three Army men were injured when militants attacked an Army patrol party in Shopian.
“Terrorists lobbed a grenade on a group of Army personnel when they were busy opening the Good Will Public School in Ahagam area of Keegam village in Shopian this morning followed by firing on Army personnel,” a police spokesman said.
He said in the incident, three Army personnel sustained injuries and were subsequently evacuated to a hospital. Their condition is stated to be stable.
He said the Army personnel exercised maximum restraint to avoid any damage to the civil population and students around.
Police have registered a case and searches to nab the militants have been initiated in the area, the spokesman said.
The attack comes a day after top officials reviewed security arrangements to ensure smooth conduct of the annual Amarnath Yatra which commenced on Thursday.