Officials said the incident was reported from the Sitagarh firing range of the force at about 1 PM when a 51mm mortar fell short of its desired target and injured the men.
The troops were on a practice session for firing mortars when the incident happened, a senior officer said.
They said the injured have been evacuated to the nearest hospital and their condition is stable.
This is the second such incident reported in the BSF in about a week's time.
On March 17, a similar accident at a firing range in Jaisalmer in Rajasthan had resulted in injuries to four personnel.
It has a training centre in Hazaribagh.