Jeremy Corbyn and Kezia Dugdale have written to Nationalist leader and First Minister Nicola Sturgeon asking her to rule out supporting the move.
The UK Government's Enterprise Bill proposes devolving the power to extend Sunday trading hours to English and Welsh local authorities.
It would mean large shops could be allowed to open longer than the current six hour restriction. There is no such restriction in Scotland.
Christian charities and the Church have resisted the move saying Sunday is a day for family.
The legislation was originally opposed by the SNP but the party has since welcomed additional protections for employees brought forward by the UK Government.
Prime Minister David Cameron has promised workers who do not wish to take shifts on a Sunday will be protected in law.
In the letter, sent before a vote on the Bill next week, Mr Corbyn and Ms Dugdale said Labour was "strongly opposed" to the Bill, which would "lead to the gradual erosion and diminution of workers' pay and rights across the UK".
In a speech to the Union of Shop, Distributive and Allied Workers (Usdaw) conference in Cumbernauld, Ms Dugdale said: "Nicola Sturgeon must not turn her back on the commitments made that her party would vote against this attack on shop workers.
"The rights of Scottish workers must not be subject to a Tory-SNP stich up in Westminster."
Usdaw general secretary John Hannett added: "Retailers have previously reduced or removed Sunday premiums to offset the costs of opening stores for longer. If that happens again in UK-wide companies, Scottish shop workers will pay the price of longer opening hours in England and Wales.
"The SNP took a strong position on protecting Scottish shop workers' pay and that threat looms as large today as it did before Christmas.
"So Scottish shop workers would feel betrayed if SNP MPs did anything other than maintain their opposition to the Sunday trading clauses in the Enterprise Bill."
Hannah Bardell MP, the SNP's business spokeswoman, said: "Our initial concern and opposition was primarily around the potential knock-on impact to Scottish workers of any changes in England and Wales to Sunday trading.
"The SNP welcome the provision for additional employee protections that the UK Government has brought forward in new schedule 1 of the Enterprise Bill, which amends the Employment Rights Act to amongst other provisions protect any worker from being forced into working on a Sunday.
"Without the strong and principled action of the SNP, such protections may never have materialised.
"On behalf of the SNP I have met with and engaged with a wide range of interested stakeholders in recent weeks and will continue to do so in the run-up to report stage of the Bill before we reach a final position."
