The new Minister for Economic Affairs, Villhelm Junnila (Finns), is to face a confidence vote in parliament called over his links to far-right groups and questionable past statements.
The chairs of the Left Alliance and Green parliamentary groups both said that Junnila would face a vote, because there was widespread disquiet among different parties about his past actions and statements.
Jussi Saramo, who chairs the Left Alliance group of MPs, told STT that even some government MPs were uncomfortable about Junnila's new job.
His Green counterpart Atte Harjanne tweeted that someone with Junnila's links had no place in the Finnish government. The confidence vote is expected to take place on Wednesday.
It was first reported by Demokraatti and Helsingin Sanomat.
The new minister has joked about his election number referencing 'Heil Hitler', campaigned at an election under the "gas" slogan and spoken at at least one event organised by a far-right group.
His ministry is responsible for the Business Finland trade promotion body, which organises trips to trading partner countries. Finland does more trade with Germany than it does with any other country.
Last week he apologised for his past actions, said he regards the holocaust as a serious matter and does not support antisemitism.