The shooting followed an altercation between the men, Maqsood ul Zaman, the police chief, said.
"Following an altercation between two troopers in the barracks, one of them opened indiscriminate fire at his colleagues," Zaman said.
The shooting occurred late Saturday at a paramilitary camp in Kulgam, south of Srinagar, he said.
In addition to those killed, a fourth soldier was wounded, Zaman said.
Kashmir has faced separatist violence for 20 years.
More than 40,000 people have been killed, according to the official count, but several human rights groups and other non-governmental organizations believe the number of dead is at least twice that amount. Read More