The minister in charge of the 20mph default speed limit will face a vote of no confidence in the Senedd next week.
Deputy Minister for Climate Change Lee Waters will face the vote of no confidence, tabled by the Welsh Conservatives, on Wednesday, 27 September.
Mr Waters is the minister in charge of the 20mph default speed limit for Wales, which came into force last Sunday.
Over 345,000 people have signed a petition to rescind the law - making it the biggest petition in Senedd history.
The motion which will be debated reads: "To propose that the Senedd has no confidence in the deputy minister for climate change given the record-breaking number of signatories to the petition: 'We want the Welsh to rescind and remove the disastrous 20mph law'."
Mark Baker, from Bridgend, is behind the petition and said he started it because he was "frustrated that the law had been introduced in just nine words in Labour's manifesto without properly explaining to people how it would impact them".
The Welsh Government says it does not plan to rescind the law and that it will save lives and make Wales a greener, healthier place.
A Welsh Government spokesperson said: "The introduction of a 20mph speed limit in mainly residential areas is designed to save lives and make our communities safer for everyone, including motorists.
"It has been thoroughly researched, voted on in the Senedd and received the backing from a majority of Senedd Members. There has been extensive consultation and it has been trialled in communities across Wales."
Want a quick and expert briefing on the biggest news stories? Listen to our latest podcasts to find out What You Need To Know…