The opposition populist right and several left-wing parties, which together hold a majority on the city council, said studies would instead be undertaken to see if the museum could stay in its current location with some remodeling and a possible expansion, or whether it would be moved to become part of the National Gallery.
The results of the studies are to be published next year.
Prior to municipal elections in September, the previous city council had decided in 2008 to move the Munch Museum into a new building housing another museum and a library.
The building was to be constructed near Oslo's new opera house, a futuristic structure that has become an architectural landmark for the city on the banks of the Oslo fjord.
The idea was to create a cultural centre to be inaugurated in 2014, when Norway will celebrate the 200th anniversary of the signing of its constitution.
But the opposition and left parties objected to the cost and the architecture of the building, among other things.
When Munch died in 1944 at the age of 80, he left around 1,100 paintings, 15,500 prints, 4,700 sketches and six sculptures to the city of Oslo.
The Munch Museum made headlines when masterpieces "The Scream" and "Madonna" were grabbed in a daring 2004 heist only to be retrieved two years later.
It has since been renovated and undergone a security overhaul, and is today home to more than half of those paintings and all of the prints.