Officials said that the boats, spotted during patrols at several points on the river in Teknaf Upazila on Sunday, were carrying at least 60 people.
As many 416 Rohingyas have been pushed back in to Myanmar between Nov 1 and 27, says the BGB.
Cox's Bazar-based BGB 34 Battalion chief Lt Col Imran Ullah Sarkar said five Rohinyas,including two minors were sent back on Sunday while crossing the border at Ukhiya's Balukhali and Bandarban's Ghumdhum.
Teknaf-based BGB 2 Battalion's Maj Abu Rasel Siddiqui said that six boats on the Naf River were stopped while trying to enter Bangladeshi waters on Sunday.
He said each of the boats carried at least 10 people.
The Myanmar army started a massive crackdown against the Rohingyas in Rakhine state after nine police officers were killed in three police outposts along the Myanmar-Bangladesh border on Oct 9.
Hundreds of Rohingyas are trying to cross the border into Bangladesh amid escalating violence. But the Myanmar government denies that Rohingya are fleeing due to its brutal crackdown.
The Myanmar army has declared the Muslim Rohingya-majority northern Rakhine as an "operations zone", where it claims to be battling Islamist insurgents.