One other person was badly wounded in Saturday's attack that was denounced by Prime Minister Elio Di Rupo, top European officials and Israeli Prime Minister Benjamin Netanyahu.
It was the first fatal attack on a Jewish center since the early 1980s in Belgium, home to some 40,000 Jews. Roughly half live in Brussels and the remainder in Antwerp.
In Israel, Netanyahu said the murder "is the result of constant incitement against Jews and their state."
The head of the EU executive Jose Manuel Barroso condemned "this terrible act" in the heart of the European capital, saying: "This was an attack at European values which we cannot tolerate."
EU foreign policy chief Catherine Ashton said there "must be no impunity for terrorism."
Interior Minister Joelle Milquet said at the scene of the attack that two women and one man were killed and another person was in hospital.
Asked whether she believed it was an anti-Semitic attack, Milquet replied that it was too early to say, but that given the target "there are strong grounds for presuming so."
The attack came on the eve of Sunday's elections in Belgium for a new federal government as well as for its regional parliaments and the European Parliament.
A deputy public prosecutor, Ine Van Wymersch, said police were interrogating a person who admitted having been at the scene at the time of the attack but denied involvement.
The person was initially interrogated as a suspect but later questioned as a witness, the public prosecutor's office said.
An inquiry was opened into "murder with premeditation".
Van Wymersch said police believed two men were involved -- one who drove away from the scene in a car and was in police custody and one who escaped on foot and who had not yet been identified.
Detectives were examining video footage.
"This is an odious attack," said premier Di Rupo. "Everything is being done... to identify and arrest its author or authors."
A Jewish community figure, Joel Rubinfeld, told AFP it clearly "is a terrorist act" after the two men were seen driving up and double-parking
outside the museum.
One opened fire, allegedly shooting indiscriminately first in the entrance hall and then further inside before getting away.
The area around the museum was closed off and security strengthened across the country in places associated with the Jewish community, Milquet said.
The shooting took place at around 4 pm (1400 GMT), with the victims apparently shot in the face and throat.
The fourth victim is in an "extremely critical" condition, Brussels mayor Yvan Mayeur told the Belga news agency on Sunday.
'Pools of Blood'
Belgian Foreign Minister Didier Reynders saw the two corpses at the entrance and said the two other victims had been shot further inside the museum.
He said he had been strolling 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 eyewitnesses.
While stopping short of calling it an anti-Semitic act, Reynders said "evidently one thinks of that."
The Jewish Museum of Belgium is in the heart of the Sablon district which is home to top antique dealers. The area is a popular weekend haunt for shoppers and tourists.
"A deeply symbolic place was struck," said Di Rupo. "The government expresses all its support to our country's Jewish community."
In 1982 a gunman opened fire at the entrance of the synagogue in Brussels, wounding four people, two seriously.