Dhaka Medical College Hospital sources confirmed that at least six people were brought in with gun shot injuries.
A rickshaw puller died from bullet wounds sustained in the crossfire.
Nabojit Khisa, a local police chief, said: "There has been a huge exchange of gunfire at BDR headquarters complex this morning. We have heard mortar fire."
Officials said that the army has been called in to bring the situation under control.
|Several people were injured in the wake of the mutiny [AFP]
Nicholas Haque, reporting for Al Jazeera from Dhaka, said there had been heavy fighting since the morning.
"The fighting broke out apparently this morning during a meeting between junior and senior officers. There is panic on the streets right now. No-one is clear about what's happening," he said.
Haque said sporadic firing was still taking place and there was chaos around the BDR compound.
Reports said that 60 officers had been taken hostage by the mutineers and four MPs, one of them a local state minister, were trying to start negotiations with them.
Couple of the soldiers told ATN Bangla, a local satellite TV channel, that they want the government to declare a general amnesty for the rebel soldiers.
Reports said that 15 representatives of the mutineers were meeting Sheikh Hasina, the Bangladeshi prime minister, after coming out of the BDR headquarters.
Imtiaz Ahmed, an international relations professor at Dhaka University, told Al Jazeera that in the past two years the border guards were used in many activities outside the role of border security, including distributing food, but "they didn't get anything in return".
"There are grievances and this [mutiny], I guess, is a result of these grievances," he said.
"...They [border guards] will engage in dialogue and I do not think they would go to the extent of forcing the army to move in violently.
"The terrain does not help in any way. The prime minister has already come out and said their grievances would be listened to and met."
The mutiny occurred a day after Hasina visited the BDR headquarters and addressed the troops, urging them to become "more disciplined and remain ever ready to guard the country's frontiers".
Bangladesh has had a history of military coups and uprisings.
Mujibur Rahman, Bangladesh's first elected president and the father of Hasina, was killed along with several of his family members in 1975.
Bangladesh, which secured its independence from Pakistan in 1971, has also experienced long spells of military rule.