The Jewish community seems like a probable target for Islamist militants who have fought in the war-torn country, as underscored by the deadly attack on Brussels' Jewish Museum in May.
"We are closed until Sunday," Oslo Jewish Museum education head Vidar Paulsen told AFP.
"It's a preventive measure we're taking in light of the shooting in Brussels."
The museum should reopen on Tuesday, since it is usually closed on Mondays.
"That's what is expected for now. We will decide later," Paulsen added.
According to Norwegian news agency NTB, the Jewish Museum of Trondheim, in western Norway, will also remain closed until further notice following police
On May 24, a man killed four people when he opened fire at the Jewish Museum in Brussels.
The suspected perpetrator is French-Algerian Mehdi Nemmouche, who spent more than a year in Syria, where he is thought to have joined some of the most radical and violent jihadist groups.
Norway is on alert since Thursday, when its intelligence service (PST) said it had "recently received information that a group of extremists from Syria may be planning a terrorist attack" in the country.
The threat is "non-specific" but "credible", according to PST chief Benedicte Bjoernland, who said it could be a question of days.
The eventual target, the timing of the attack, the identity of the militants and their location, are not known, she added.
PST analysis head Jon Fitje Hoffmann told local TV channel TV2 Nyhetskanalen that there were indications that the group of individuals had already left Syria with the aim to "perpetrate a terrorist attack in the West", with Norway being "specifically mentioned".
At a press conference on Friday, Odd Reidar Humlegaard, head of the police directorate, said that it was "more likely that nothing happens than that something actually happens".
"But this time around, we will be more prepared than ever to handle the situation if it occurs," he added in an implicit reference to the massacre by right-wing extremist Anders Behring Breivik, who killed 77 people on July 22, 2011, when police were heavily criticised for their slow reaction.