After the body of the slain militant was handed over to his family for the final rights, all educational institutions across Jammu and Kashmir were shut down.
Mobile Internet services were snapped across the valley to maintain law and order. Even speed of fixed landline broadband connections were reduced to prevent uploading of inflammatory posts and pictures.
Heavy deployments have been made in capital city Srinagar, south Kashmir's Pulwama, Anantnag, Shopian and Kulgam districts among other areas.
Musa was killed late on Thursday by security forces in Pulwama district when security forces had launched a cordon and search operation in Dadsara village of Tral area following information about militant presence.
"The trapped militants were persuaded to surrender. Instead they hurled grenades and started a gunfight, triggering an encounter," a source said.
One of the dead was identified as Zakir Musa, a close associate of Burhan Wani who was killed in 2017.
Real name, Zakir Rashid Bhat, Musa was a militant of Hizbul Mujahideen who succeeded Burhan and later headed the Al Qaeda affiliate. He had taken to militancy in 2013.
An engineering student in Chandigarh who abandoned education and joined militancy, Musa was born in Noorpora village of Tral area. His father, Abdul Rashid Bhat, is a senior engineer working for the Jammu and Kashmir government.
The killing of Musa is seen as a big success for the security forces in their anti-militancy operations in Kashmir.
After Burhan Wani's death, Zakir Musa threatened to behead Kashmiri separatist leaders of the Hurriyat Conference for calling Kashmir a political dispute instead of a religious struggle to establish an Islamic state.
( With inputs from IANS )