The vote, centred on Finance Minister Riikka Purra and Economic Affairs Minister Wille Rydman of the far-right Finns Party, is widely seen as an embarrassment to the government but is not expected to bring down the cabinet or force the pair out.
Within days of assuming power this summer, the four-party, right-wing government was in turmoil after Finnish media revealed old writings by several Finns Party ministers that were deemed racist by critics.
In an attempt to stave off collapse, the government last week agreed on a policy to combat intolerance and brought it up on Wednesday for a plenary discussion in parliament.
But the promise of a new focus on anti-discrimination was "too little too late", the leading opposition Social Democrats (SD)said.
"The government is incapable of showing they have renounced racism," said Nasima Razmyar, an Afghanistan-born member of Finland's parliament who proposed the no-confidence motion on behalf of the SD.
The vote, which is expected to take place on Friday, will also included separate votes targeting Purra and Rydman individually, according to the SD as well as the Greens and the Left Alliance which gave their backing to the motion.
But the three opposition parties only have 67 seats combined in the 200-seat parliament, while the government commands 108 seats, making it unlikely that the motion will pass.
Purra, who is the Finns Party's leader, apologised in July for anonymous comments she acknowledged she had posted online about 15 years ago - though she said many had been taken out of context.
The Finns Party's first economy minister Vilhelm Junnila had to resign at the end of June, just 10 days into his term in office, after being accused of having made repeated Nazi references.
The party soon replaced him with Rydman, whose former girlfriend then leaked to Finland's largest daily Helsingin Sanomat his private messages that contained racial slurs.
(Reporting by Essi Lehto and Anne Kauranen, editing by Terje Solsvik and Angus MacSwan)
By Essi Lehto and Anne Kauranen
