Head Constable Vedpal Singh and Constable Rajesh Kumar were injured when the hand grenade exploded close to them, SHO (Mandore) Kamal Singh said.
The condition of Vedpal, admitted to a private hospital, was stated to be serious, the SHO said adding he had suffered injuries in hands, cheeks and head.
A BSF official said it was a premature explosion during the routine practice at the firing range and a probe had been initiated into the incident.
Recruit Rajesh Kumar threw the grenade in the air but it exploded before time close to him, he said.
Rajesh and instructor Vedpal were injured, the official said.