Sham Sunder of the 44 Rashtriya Rifles (RR) was killed in the gun battle in Aglar village with the militants who belonged "to the same group" who attacked a police check-post in Rajpora on Saturday.
Two other soldiers and a civilian were also injured in the operation that has now ended, police said. A cache of arms and ammunition was recovered from the slain militants.
Following intelligence inputs about the presence of militants, troops of the 44 RR, Special Operations Group (SOG) of state police and the Central Reserve Police Force (CRPF) had surrounded the village on Monday evening.
As the cordon was being tightened, hiding militants fired at the joint team of security forces. The gunfight started late on Monday evening.
The civilian injured is Showkat Ahmad, who along with other protesters had clashed with the security forces to disrupt the terror operation.
Three weapons, including one AK, one M16 rifle and one pistol, besides ammunition were recovered from the encounter site, said a police spokesman.
Internet services have been suspended in Pulwama district to check the spread of rumours.
The injured were sent to hospital. Identification of the dead bodies was underway.