The incident took place at around 1 am after a reported scuffle between the jawans, sources said.
"An SSB soldier, identified as Vijay Kumar, opened fire from his service rifle on his colleagues. Two soldiers have died while two others have been injured in the shooting," Superintendent of Police (SP) Kulbir Singh said.
Vijay Kumar has been arrested and is being interrogated.
The four SSB jawans were rushed to the Kishtwar district hospital, about 220 km from Jammu, where Narinder Singh, who belongs to Uttarakhand, was declared dead. His colleague Veer Singh succumbed to his injuries later.
The two other injured SSB troopers - Ravinder Nath and Habib-ul-Islam - are undergoing treatment for bullet injuries at the hospital. Habib got injured when he tried to grab Vijay Kumar.
The SSB has been camping for the last two months at the police line in Kishtwar after the central government decided to replace Central Reserve Police Force (CRPF) with SSB for internal security in some troubled areas of the state.