According to officials, Sepoy Ajay Kumar was found dead near SAIL Chersoo in Awantipura after gunshots were heard at around 1:55 am.
"In 15 days, our jawans conducted surgical strikes and air strikes, entered Pakistan's home and eliminated the terrorists and tore apart their hideouts of these terrorists," he added.
A case has been registered. Further investigation is on.
Officials said the curbs on the movement of people were in force in parts of Srinagar, and Kulgam and Pulwama towns.
Musa was killed on Thursday night but his body could be retrieved only by 6 am, after which Army spokesman Colonel Rajesh Kalia confirmed his killing.
As a precautionary measure, the authorities have ordered closure of all schools and colleges across Kashmir on Friday and were also expected to order restrictions.
The restrictions on the movement of civilian traffic on the Jammu-Srinagar Highway were placed on April 7 to prevent Pulwama type terror attack on convoys of security forces.
"Three terrorists have been killed in Panzgam operation. Weapons and war-like stores were recovered," Defence Ministry Spokesman Colonel Rajesh Kalia said.