The woman, identified as 24-year-old Rubi Jan, sustained a gunshot injury during protests in Batmuran village during the encounter between the holed up militants and the security forces, the police said.
Nine protesters were also injured in the clashes. The injured Jan was shifted to hospital where doctors declared her “brought dead”.
The third militant sustained a minor injury but was still engaged in the gun battle.
Director General of Police S.P. Vaid said one of the slain militants was from the area.
The gunfight started on Monday evening when troops of the Rashtriya Rifles (RR) and Special Operations Group (SOG) of the state police surrounded a house where the three were said to be hiding.
The hideout was destroyed in the fight.
Authorities have suspended Internet services in the south Kashmir region to check the spread of rumours.