Joanna Cherry has called for SNP members to get a new vote on whether the party should continue with its governing pact with the Greens.
The Edinburgh South West MP, who is chair of the Commons human rights committee, said the Greens were "deeply unpopular" and said the alliance between the parties was a "problem".
Ms Cherry, a KC, said the SNP would have to chuck the Greens "to recover as a party".
She tweeted on Monday: "SNP members should get a 2nd vote on [the Bute House Agreement].
"If we are to recover as a party from current challenges we need to address problems like this alliance with a deeply unpopular party on the doorsteps rather than sweeping them under the carpet as per previous practice."
The SNP and the Greens signed the Bute House Agreement (BHA) in 2021. It gave the two parties a majority in Holyrood and put the Greens in the Scottish Government for the first time.
But Green members are furious after the Scottish Government last week ditched a target to reduce carbon emissions by 75% by 2030.
The party is to hold an extraordinary general meeting (EGM) on the BHA at the end of May with both co-leaders Patrick Harvie and Lorna Slater arguing to continue with the arrangement.
Under the pact, both Ms Harvie and Ms Slater are junior ministers in Humza Yousaf's government.
In return, Scottish Green MSP must support the government on key votes such as the Budget and in confidence motions.
Ms Cherry is the latest SNP figure to raise concerns about the impact of the agreement on the SNP.
Former rural affairs secretarty Fergus Ewing has repeatedly called for the SNP to withdraw from the pact, while former finance secretary Kate Forbes last year suggested it should be put to SNP party members whether to continue the agreement when they met for their annual conference last October.
Former health secretary Alex Neil today called for the two parties to "go their separate ways".
Mr Ewing has previously described the Scottish Greens as "hard-left extremists who should never be anywhere near government".
SNP spokesperson: “Individuals are at liberty to express their thoughts on social media. SNP members voted overwhelmingly to support the Bute House Agreement in 2021.”
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