The bomb, believed to be an improvised explosive device (IED), went off at about 9 AM.
The injured girl, identified as Tinoi (7) of Moirang Purel Village, was taken to an Imphal Hospital.
Earlier reports said the injured child was a boy.
The BSF had come under attack on previous occasions as well.
Two BSF personnel were injured at Kangpokpi area in Senapati district on Monday last.
On May 20 last, a BSF convoy on foot patrol was ambushed by militants armed with rocket launchers and sophisticated automatic weapons in Thoubal district of Manipur but there was no casualty.