The government was expected to commit €40 million (£34 million) of public money towards the construction and running costs of the Guggenheim Helsinki, which has an estimated build cost of €130 million (£110 million).
But during recent budget talks the nationalist Finns Party – which forms part of the country's coalition government, alongside the Centre Party and the National Coalition Party – objected plans to publicly fund the project.
"This is the end of the matter, we have ruled out state funding [for Guggenheim] once and for all, for this government," parliamentary head of the Finns party Sampo Terho told Reuters.
"We are not opposed to the project as such, we just don't think it is something that the state should participate in."
On his personal blog, party leader Timo Soini also rejected state funding of the project. He said that while the party would not be opposed to a privately funded Guggenheim Helsinki, it did not support plans by fellow coalition politicians to contribute €40 million (£34 million) of public money to the scheme.
"The Centre Party and the National Coalition Party go back to state-funding Guggenheim, despite the fact that we have agreed otherwise a number of times," he said, as translated by the Helsinki Times.
"There will be no money for the project. It will not even be discussed in the budget session."
Parisian practice Moreau Kusunoki Architectes won the contest to design the new major outpost for the American arts institution in 2015, seeing off competition from over 1,700 entrants.
The winning design comprises a cluster of charred timber pavilions with concave roofs that are to be linked by garden patios.
A lighthouse-light lookout tower would rise from one side of the site to provide views over the city's waterfront.
The project is expected to generate a significant amount of revenue from tourism, doing for Helsinki what the Frank Gehry-designed Guggenheim has done for the Spanish city of Bilbao.
It is the latest in a series of outposts proposed by major museums. The V&A is opening new buildings in east London and Dundee, while the Louvre opened a new building in Lens in 2012 and has a new building underway in Abu Dhabi.