The public transport was off the roads and only private vehicles and some three-wheelers and cabs were plying.
One of the two killed was hit in crossfire between security forces and militants.
Following a separatist appeal for a protest shutdown across the Kashmir Valley, authorities on Monday made heavy deployment of security forces to avoid violence, police said.
The suspected militants had taken refuge in Frisal village when they were surrounded by police and the military, officials say.
He said the security personnel were also deployed in strength in other vulnerable areas including downtown Srinagar to keep watch on the situation and prevent flare-up in the situation.More news: Quake kills at least six in southern Philippines
She was lodged in Woman Police Station at Rambagh in uptown city.
Meanwhile, the strike called by separatist groups to protest the civilian killings evoked mixed response today. Clashes between protesters and security personnel erupted in Palhallan area of Pattan, Baramulla district, after the Zuhr prayer (noon prayer) on Monday, when protesters raising anti-India and pro-freedom slogans started marching towards the Srinagar-Muzaffarabad highway. Three terrorists managed to escape. The police had to resort to force to disperse the crowd.
Officials say the civilian who died was inside the house which came under fire from the security forces.
"We have directed men and officers on the ground to exhibit maximum restraint and avoid using excessive force", he said.
Life in south Kashmir districts of Kulgam, Anantnag, and Shopian was adversely affected because of the tension following the separatist call to march.