Lord Forsyth of Drumlin delivered the withering put down to the fiery First Minster over her “antics” over Britain’s EU departure.
Referencing Scotland’s rising unemployment rate and health care problems the peer said Ms Sturgeon should “stick to her day job”.
Lord Forsyth, speaking during a debate in the House of Lords on the impact of Brexit, said: “One thing that the Liberals and the SNP have in common is that they are crying out for more referendums, but at the same time won’t accept the result of referendums when people actually vote.
“I suggest to the First Minister that she sticks to her day job and concentrates on unemployment and the problems in the health service and the problems in education and the problems elsewhere, and perhaps doesn’t get involved in foreign affairs.”
The 62-year-old continued: “I suggest her expertise may not lie in that area and she should butt out of this particular debate.”
Lord Forsyth suggested Nicola Sutrgeon 'butt out' of Brexit
Lord Forsyth, who served in John Major’s cabinet between 1995 and 1997, said he wanted to see a speedy solution to the question of EU nationals residing in Britain and Britons living in EU nations overseas.
He said: “The way to resolve it quickly is to get on with moving Article 50 and persuading our colleagues in the European Union that we need a reciprocal deal.
“That those British people living in the European Union are able to stay in the European Union and likewise people who have come here will be able to stay.
“Nobody seriously thinks that more than three million people are going to be expelled from this country.”
On Thursday Brexit secretary David Davis accused the SNP of behaving in a “holier than thou” manner over EU nationals.
Theresa May's Brexit strategy has frustrated Ms Sturgeon
Theresa May's 12 point Brexit plan
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Continued cooperation with the EU to tackle terrorism and international crime.
I suggest her expertise may not lie in that area and she should butt out of this particular debate
The Brexit Secretary suggested MPs should be “reminded of the words of Nicola Sturgeon during the independence referendum in 2014” when she warned keeping an independent Scotland outside of the EU could see EU nationals lose their right to stay in Scotland.
At the time, Ms Sturgeon had warned: “We have set down a robust and common sense position.
“There are 160,000 EU nationals from other states living in Scotland, including some in the Commonwealth Games city of Glasgow.
“If Scotland was outside Europe, they would lose the right to stay here.”
During First Minister’s Questions on Thursday, the other party leaders in Scotland urged Ms Sturgeon to end her “obsession” with independence.
Scottish Conservative leader Ruth Davidson told her at Holyrood: “I want a country that is run by a Scottish Government that spends it’s every waking hour sorting out public services and not obsessing about another referendum.
“A Scottish Government that actually wants to deal with the child obesity crisis, not one plotting how Brexit can be used to create more division and uncertainty in Scotland, that’s the country that I want back.”
Labour’s Kezia Dugdale added: “She should stop the grandstanding on Europe, end the games on independence and tell us this: what really is the SNP’s top priority – is it closing the gap between the richest and the rest, or is it just another divisive independence referendum?”