There are no reports of any casualties yet in the gunfight at the Bangladesh Rifle headquarters, officials say.
The BBC's Mark Dummett, in Dhaka, says that reports suggest the clashes are between officers and soldiers of the paramilitary force.
The army has been called in to deal with the situation, officers say.
Our correspondent says that some local TV channels are speculating that it is a mutiny by soldiers over a pay dispute.
Colonel Rezaur Rahman, deputy chief of Bangladesh's internal security force, the Rapid Action Battalion, told the AFP news agency: "The army has been called in. They have already started moving to the area."
The Bangladesh Rifles headquarters - the force protects the country's borders- is located in the Pilkhana area of Dhaka.
One report said that the gun battle coincided with a meeting of senior Bangladesh Rifles officers.
Reports say that smoke is coming out of the complex and security forces have cordoned off the area.
"There has been a huge exchange of gunfire at the headquarters. We have heard mortar fire," local police chief Nabojit Khisa told the AFP news agency.
He said police were not being allowed to enter the complex.
There is no information yet on casualties, but reporters say some civilians walking past the camp have been hit.
TV pictures from a Dhaka hospital showed some civilians injured in the gun battle being wheeled in.
There are unconfirmed reports that soldiers have also opened fire on a helicopter patrolling above the camp, where the fighting is taking place, our correspondent says.
