With almost two-thirds of Scots having voted to remain in the 2016 referendum, Catherine Stihler warned Labour would “pay the consequences electorally at the hands of the SNP” if it ignored that result.
Party leader Jeremy Corbyn said it would be “wrong” for the UK to sign up to membership of the European single market if this would prevent a future Labour government from implementing “radical plans”.
However, Ms Stihler insisted the option of keeping Britain in the single market, which permits the free movement of goods and people, must remain on the agenda.
She made the comments at a fringe meeting at the Scottish Labour Party conference in Dundee, where she clashed with former Labour MP Ian Davidson.
The former Glasgow South West MP, who lost his seat in 2015, said it was “totally false” for those who wanted Labour to back single market membership to state they were being denied a vote on this at the conference.
While several motions calling for the party to back this position were submitted, a “unity motion” from Labour’s Scottish Executive, which crucially contains no mention of the single market, will be voted on at the conference on Sunday.
Mr Davidson said: “It is totally false to suggest those who supported the single market resolutions are not being given a vote.”
Labour MP Ian Murray and former Scottish leader Kezia Dugdale are among those who want the party to back staying in the single market.
Ms Stihler argued this was “absolutely critical to mitigating the worst effects of the situation we find ourselves in”.
The Scottish MEP said: “I want to be very clear - there is no such thing as a good Brexit. All Brexits are bad for jobs, bad for jobs and bad for our society.”
While Labour now backs remaining in a customs union with the European Union after Brexit, Ms Stihler said the party also needed to embrace single market membership.
She said: “Labour is going down the right path advocating a customs union but what we really need to do is to have security being part of the single market brings.
“If we do not do this, do not take take time, then as as Labour Party and movement we run the risks of us crashing out of the EU, our biggest trading partner and most important ally in a world currently in flux with Donald Trump threatening trade wars.
“Then we turn to Scotland and we should be in no doubt if we do not reflect how the majority of people voted, which was to remain part of the European Union, we will pay the consequences electorally at the hands of the SNP.”
Ms Stihler said she had fought to ensure the single market membership was in the motion party activists will vote on.
“I think we have to have every single option left open to us,” she stated.
“There is no such thing as a good Brexit but if we can be part of the single market and part of the customs union, it will certainly help to protect jobs and livelihoods.
“We have to keep the single market on the agenda. That’s something I will be advocating for.”