The Rapid Action Battalion raided a village near the border with Myanmar late Monday to free the Rohingya Muslims who had been held there for a day, said Major Ruhul Amin.
The RAB chief who led the operation at Sabrung near Cox's Bazar told AFP the 20 included seven women, five men and eight children.
"They were held there by a gang of boat owners and crew who demanded 20,000 taka (RM1,035) per person for a two-hour boat ride from Myanmar," he said.
A boat ride between Maungdaw and Bangladesh's main landing station at Shah Porir Dwip would cost no more than five dollars normally.
Amin said they arrested three members of the gang for profiteering.
The UN estimates that 507,000 Rohingya Muslims have fled Rakhine into Bangladesh since late August after the latest eruption of violence in the northern Myanmar state.
Many have arrived on rickety boats crossing the Naf river, which marks the border between Bangladesh's Cox's Bazar district and Rakhine.
Police said boat owners, crew and fishermen have charged exorbitant prices for the rides.
"It has become a common phenomenon" since the influx began, Amin said.
Authorities have deployed mobile courts to crack down on the profiteering gangs and handed down sentences of up to six months' jail on nearly 200 people.
"We have arrested 20 brokers and freed nearly 2,000 people in raids in the coastal villages. In one raid we rescued about 1,000 Rohingya who were held at six houses," Amin said.
Rohingya who fled to Bangladesh said the boatmen extracted every last penny from them for the ferry and threatened to throw them overboard if they refused to surrender valuables including gold ornaments
Media reports have mentioned Rohingya being held by boatmen and agents for hours in coastal villages until they made inflated payments for the trip.
Rohingya living in established refugee camps in Bangladesh have also been accused of joining the profiteering.