A fourth person was seriously wounded, emergency services said.
Belgian broadcaster RTBF said the shooting had taken place inside as well as outside the museum.
Deputy Prime Minister Didier Reynders, who was one of the first people to arrive at the scene, said he was shocked by the attack.
The gunman arrived at the museum at around 15:50 (13:50 GMT) carrying a backpack, then opened fire before fleeing in a car, Belgian media reported.
Brussels Mayor Yvan Mayeur said three men and a woman had been caught up in the attack. “It’s clearly extremely serious,” RTBF quoted him as saying.
A number of people were treated for shock after the shooting in the central Sablon area of the city.
Prime Minister Elio Di Rupo expressed his condolences and support for the victims’ families.