Shadow Scottish Secretary Margaret Curran challenged the SNP leader on the issue as supermarket chiefs were said to have suggested that if Scotland left the UK following next year's referendum, this could impact on costs.
The Scottish Government has insisted there is "no reason" why prices would be higher under independence.
But Asda chief executive Andy Clarke said: "We believe in fairness so the price customers pay for a pint of milk or loaf of bread is the same regardless of where they live in the UK. However the cost of doing business in different parts of the country does vary.
"A Yes vote in 2014 could result in Scotland being a less attractive investment proposition, and put further pressure on our costs."
Ms Curran said: "These important comments from top supermarkets as people go about their Christmas shopping show the benefits to Scottish families of being part of the UK.
"The message from supermarket bosses is clear - the cost of doing the weekly shop in Scotland is cheaper as part of the UK and would be more expensive with independence."
The Labour MP added: "Today the cost of doing business is shared by shoppers across the whole of the UK, keeping down costs here in Scotland.
"This is a strong positive example of the benefits we get as part of the UK. Why would we want to give this up?"
However a Scottish Government spokeswoman said: "There is no reason why retail prices in an independent Scotland would be any higher than at the moment."