In the application to start the school, the Association of Muslim Mothers said that the school would teach its pupils Arabic and Islamic values as well as the standard subjects on the curriculum, replacing the subject of Religion, Philosophy and Ethics with Islam, Religion and Philosophy.
The school aims to have 200 students, and is expected to look for premises in the east side of Oslo, where most of the city's immigrant population lives.
Both Norway's opposition Labour Party and the anti-immigrant Progress Party, which is part of the government coalition, spoke up against the plans.
"I'm concerned that if we begin to group ourselves by religion, it will weaken the inclusiveness of Norwegian society," said Trond Giske, the Labour MP who chairs the Norwegian parliament's education committee. "We spend a lot of money on inclusion in Norway, and now we are apparently going to be spending it on segregation."
"These kids need to be in an environment with other Norwegian children," said Camilla Wilhelmsen, who leads the Progress Party in Oslo. "The community is already to some extent segregated and this will not make it any better."
The Association of Muslim Mothers has fought for more than a year to open the school and has had its application turned down several times.
Today, Oslo has a Muslim kindergarten, the Mosaikk Barnhage, but no Muslim schools.