The incident took place at about 8:30 am when a 51mm mortar fell short of its target at the forces' firing range in Kishangarh.
The six personnel suffered injuries due to the blast of the ammunition, out of which two are critical, a senior BSF officer said.
The troops were participating in a firing exercise.
Officials said one of the critically injured personnel will be air evacuated to a hospital in Jodhpur while others are being treated here.
Few days after this, six men of the paramilitary were injured in similar circumstances during mortar firing exercise at its centre in Jharkhand's Hazaribagh.
The BSF is deployed in Rajasthan as part of its task to guard the India-Pakistan International Border (IB).