"Two women and one man are dead, a third person is in hospital," Interior Minister Joelle Milquet said at the scene. "We don't yet know if they were tourists or staff, they haven't been identified."
Asked whether she believed it was an anti-Semitic attack, she said it was too early to say as a police and judicial inquiry was under way but that given the target "there are strong grounds for presuming so".
A Jewish community figure, Joel Rubinfeld, told AFP it clearly "is a terrorist act" after two men were seen driving up and double-parking outside the museum.
Rubinfeld, who heads the country's anti-Semitic League, said the act was the result of "a climate of hate."
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Reports said the driver has been picked up within three hours of the shooting, which took place at around 4 pm (1400 GMT). There was no confirmation from police.
A bystander, Alain Sobotik, told AFP he saw the corpses of a young woman and a man just inside the doors of the museum.
A picture shows them lying in pools of blood.
Also at the scene shortly after the shooting was Belgian Foreign Minister Didier Reynders who told reporters that the two other victims had been shot inside the museum.
Reynders said he had been nearby when he saw people fleeing and heard shots and rushed to help.
When he saw "bodies on the ground in pools of blood" he called the 112 emergency number and rounded up eye-witnesses to assist the police.
"I am shocked by the murders committed at the Jewish museum, I am thinking of the victims I saw there and their families," Reynders said on Twitter.
The Jewish Museum of Belgium, which was not answering calls, is located in the heart of the Sablon district which is home to the city's top antique dealers.
Police quickly cordoned off the area. The head of Belgium's Jewish Consistory told La Libre that "it is probably a terrorist act. For us it is an extremely serious act."
He said the museum had received no recent threats and that its staff "are in shock".