Former Scottish Secretary Jim Murphy, who now serves as Labour's shadow defence spokesman at Westminster, makes the astonishing claim in a magazine interview.
Mr Murphy is known as a regular church goer and he was seen warmly greeting the Pope during last year's Scottish visit by Benedict XVI. In the article, he makes it clear he doesn't believe Britain is ready for a Catholic at the top of government.
Ruling himself out for the top job, he said being Scottish is no bar to entering No. 10. But Mr Murphy added: ''You can be a Scot and be Prime Minister.
But can you be a Catholic and Prime Minister of the United Kingdom?''
Before the United Kingdom was formed in 1707, the English Act of Settlement and Scotland's Act of Succession barred Catholics from taking the throne.
That led to the toppling of the Stewart dynasty to make way for their Protestant, Hanoverian cousins.
Three hundred years later the controversial rule is still in place, although protests have continued to grow.
But there there is no legal block on Catholics holding any government post.
Holyrood MSPs called for the bar on Catholic royals to be lifted in a unanimous vote, but only Westminster can change the rule.
While there has never been a Catholic Prime Minister, Tony Blair attended Mass alongside his Catholic wife and children, but he chose not to convert until after he left office.
Tory chief whip David McLetchie said: ''Jim Murphy is being overly negative. In the 19th century people thought a Jew couldn't be Prime Minister. Disraeli and the Conservatives proved them wrong.
Opportunity
''In the 20th century some thought a woman couldn't be Prime Minister. Mrs Thatcher and the Conservatives proved them wrong. If Mr Murphy feels being a Catholic in the Labour Party is a barrier to becoming Prime Minister in the 21st century perhaps he should rethink his political ideas and join the real party of opportunity for all.''
MSP Michael McMahon, one of Holyrood's most prominent Catholics, said: ''I've got 35 people who could lose their jobs at Warburton's Bakery in my constituency. Some of them might be Catholics, some of them might not. I'll fight for them, but fighting over the Act of Settlement — forget it.''
A spokesman for the Catholic Church in Scotland said: ''The only parallel to these comments is that Tony Blair did not become a Catholic until after he stood down as Prime Minister. He could have stayed in office and become a Catholic — there is no legal bar. However, Jim Murphy's comments do give an insight into a more insidious climate of religious intolerance within the British state. It is the bedrock of discrimination against Catholics within the establishment of this country.''