The clash occured in the southern Kashmir district of Poonch, a police spokesman said. Troops have launched a search in the Indian-controlled region for the rebels.
Earlier, Indian troops shot dead three Muslim rebels in two separate encounters around Kulgam township overnight, 60km south of Srinagar.
One of the slain rebels was identified as Umar Pathan, a Pakistani, the spokesman said. A soldier was also killed during one of the gun battles.
Two more rebels were shot dead in the northern district of Kupwara late Tuesday evening. Police identified one of the slain rebels as Vilayat Khan, the divisional commander of a hard line rebel group Tehrik al-Mujahidin.
Civilian mine death
Security forces also shot dead a separatist in southern Udhampur district, while suspected rebels shot dead two civilians in the districts of Pulwama and Rajouri overnight, police said.
Separately, a civilian injured in a mine explosion in northern Bandipora township last week died in a Srinagar hospital on Wednesday, police said.
And a child was injured overnight when rebels bombed the office of a television cable network in Sopore town, 50km north of Srinagar.
Officials say more than 38,000 people have died in Indian Kashmir since the eruption of an anti-Indian rebellion there in 1989. Separatists put the toll between 80,000 and 100,000.