Ms Mowlam suggested that old palaces be used as public museums and galleries.
In an interview with Saga magazine, she said: "I don't suggest that the Royal Family should close down and shut up shop, but if people want a monarch of the new century, they should have a palace of the new century, in line with the architecture you see around London."
Her comments have been condemned by Conservatives as inappropriate.
The former Northern Ireland Secretary has caused controversy with her views on the Royal Family before.
Six years ago, as a shadow minister, she said that the monarchy should leave Buckingham Palace and Windsor Castle for a new People's Palace.
Later, on BBC radio, she predicted there would "evolutionary change" in the 21st century.
And she added: "It's a personal view and not a government view. I just put my personal views on the record six years ago. I am not reneging on them. I said it.
"I still think that modernisation and change is the way forward and I made this as a suggestion for the 21st century. I didn't intend to make it a major news story."
Influential woman
Recently, Ms Mowlam was judged more influential than the Queen in a list of Britain's 100 most powerful women compiled by Good Housekeeping magazine last October.
Ms Mowlam made it clear she has no personal dislike of the royals.
"I am not a great fan of the monarchy, even though I like Prince Charles and I like Princess Anne, and exchanges I have had with the Queen have been very pleasant.
"But in terms of constitution, I would support a change. The public aren't of a like mind yet, so it won't happen yet. But it will come. It will evolve. I think the Queen realises this.
"That is why Prince Charles is becoming a potential leader of the people."
'Ridiculous and wrong'
Constitutional historians condemned Ms Mowlam's remarks.
Lord Blake branded them "absolutely ridiculous". He said: "It is no business of Mo Mowlam where the Royal Family live. If the Royal Family wanted to move out, then that would be up to them.
"But they have made Buckingham Palace much more open to the public than it
ever has been in the past."
"Either it is government policy or it is not - cabinet ministers cannot have personal views," he said.
"I agree that radical constitutional change may be needed, but this should be done publicly and with careful thought - which is not what Mo Mowlam is doing."
Blair 'monarchist'
A spokesman for Tony Blair said: "The prime minister is an ardent supporter of the monarchy.
"The Queen lives in Buckingham Palace and I don't think she's intending to move and the prime minister doesn't think she should."
The spokesman said that Mo Mowlam was an important cabinet member and was held in high regard by Mr Blair.
And Deputy Prime Minister John Prescott played down the row, saying: "She (the Queen) has been modernising, she has been changing, but it is a decision for her - hardly the biggest issue of the year, is it?"
'Grace and favour' apartment
However, anti-royalist MP Dennis Skinner (Lab, Bolsover) went further than Ms Mowlam.
He said: "Some of us believe the monarchy should be abolished, and a lot of the polls show that 30%-40% of the population think that as well.
"If the government wants to kill two birds with one stone, I suggest that they move the royals out to the Millennium Dome."
Liberal Democrat MP Norman Baker said it was "a classic case of the pot calling the kettle black".
"Ms Mowlam's comments would have more weight if she didn't have the use of a grace and favour apartment in London courtesy of the taxpayer," he said.
A Buckingham Palace spokeswoman said: "Dr Mowlam's comments are entirely a matter for her. It would not be appropriate for me to comment."