Belgian authorities said on Tuesday they were investigating a suspected arson attack on a synagogue in the capital Brussels, but did not believe it was "terrorist" related.

Jewish community officials said it was not immediately clear whether it was an anti-Semitic attack, although the building had been the target of petrol bombers in 2010.

The wife and two children of the synagogue's caretaker suffered slight smoke inhalation in the fire on the top floor of the building, where they lived, said a fire department spokesman quoted by the Belgian media.

The caretaker was absent at the time.

Laurens Dumont, a spokesman for the city prosecutor, said "it would seem that the fire was set deliberately" at the synagogue in the neighbourhood of Anderlecht near the main train station, but the investigation was in its early stages.

"All leads are open," Dumont said.

The city prosecutor's office said in a statement later "there was no reason to suggest that it was a terrorist attack," months after four people were shot dead at the Jewish museum here in an apparent Islamist militant attack.

The fire department spokesman said arsonists started the fire in the fourth floor of the synagogue in the early hours of Tuesday.

An official from the neighbourhood's Jewish community, Jehuda Guttman, told Belgian media he did not know for now whether the event was anti-Semitic.

"If this act had been anti-Semitic, the perpetrators would have burned the Torah, sacred books. And that's not the case. I can only guess. Here, we live in peace with everyone," he said.

The fire came just two days after the reopening on Sunday of the Jewish Museum in Brussels, where four people were shot and killed on May 24.

Mehdi Nemmouche, a Frenchman of Algerian descent allegedly aligned to the jihadist Islamic State, is being held in Belgium suspected of carrying out the murders.

He was arrested six days after the shooting in the southern French port of Marseille and later extradited to Belgium.

Belgian Prime Minister Elio Di Rupo said he was "troubled" by the fire "and I forcefully condemn this criminal act."

He repeated the appeal he issued on Sunday's reopening of the Jewish Museum of Belgium.

"All anti-Semitic or racist attacks or behaviour must be vigorously condemned, prosecuted and punished," Di Rupo said on Twitter Tuesday.

On Sunday evening, stones were thrown at a group visiting the National Memorial to the Jewish Martyrs of Belgium, which is also located in the Anderlecht district.