The incident took place at around 7.15 pm and the police is investigating the cause of the firing, Senior Superintendent of Police (SSP), Ramban, Mohan Lal told PTI.
"An SSB head constable suffered a fatal casualty in the brief firing while another jawan lost his jaw bone due to an attack by some blunt object," Mr Lal said.
The constable killed had got one gun shot and his body was taken to the hospital for post-mortem, officials said, adding the injured jawan was also evacuated to a hospital for treatment.
"It is premature to say anything about the incident right now. We are ascertaining the details," the SSP said while not ruling out either a terrorist attack or fratricide.
The jawans were manning a post outside an 8.5 km-long under-construction tunnel connecting Banihal town of Ramban district in Jammu province with Kulgam district's Qazigund, the gateway to the Kashmir valley.