In Srinagar, the officials said, "strict restrictions" were in place in Nowhatta, Rainawari, Khanyar, Safakadal and M R Gung police station areas, while "partial restrictions" were in force in Maisuma and Kralkhud areas.
The officials said security forces have been deployed in strength in other parts of the valley to avoid any untoward incident.
Musa, the so-called head of the Ansar Ghazwat-ul-Hind, was killed in the encounter at Dadsara village of Tral in the south Kashmir's Pulwama district on Friday after forces launched a search operation on late Thursday evening following specific information about the presence of militants there.
The officials said efforts were made to make Musa surrender, but the request fell on deaf ears and he lobbed grenades on the forces using a launcher, triggering a gunfight in which Musa was killed in the early hours of Friday.
His killing led to spontaneous shutdown and protests in the valley.
Meanwhile, most of the shops, fuel stations and other business establishments remained shut in the valley due to a strike called by hardline Hurriyat Conference chairman Syed Ali Shah Geelani against the killing of Musa and a civilian Zahoor Ahmad, a resident of Naira Pulwama who was killed by unidentified gunmen on Thursday, the officials said.
They said public transport was off the roads, but few private cars and auto-rickshaws were seen plying.