Demos director Tom Bentley, a former adviser to Home Secretary David Blunkett, and head of strategy James Wilsdon, also want a compulsory retirement age for Britain's monarchs.
By staying on the throne, the Queen is stifling debate about the monarchy, they argue in a new essay collection.
"Quit while you're ahead, Ma'am," they urge.
The pair suggest Prince Charles might not become king until he is almost 80 if his mother does not stand aside.
That is something that risks the monarchy becoming an institution of the elderly, they continue.
Preparing the heir
In their essay, Mr Bentley and Mr Wilsdon dub themselves "The New Monarchists".
A mandatory retirement age could help future heirs to become better prepared to become king or queen and ensure the succession was "properly managed".
The Queen continued her Jubilee tour of the UK with a visit to the Scottish Parliament on Tuesday as she celebrates 50 years on the throne.
Earlier this year she quashed any suggestion she might abdicate by vowing to "continue serving the people of this great nation of ours".
In their essay, Mr Bentley and Mr Wilsdon say: "There is something absurd about someone declaring they intend to go on forever.
"If the Queen lives as long as her mother, Charles would be nearly 80 by the time he reached the throne.
"Britain is in danger of replacing the monarchy with gerontocracy."
Modernisation call
"By saying that she plans to stay on the throne, she is silencing the debate about the future of the monarchy at the very moment when it needs to be opened up," they say.
The Queen's abdication would allow a new focus on longer-term modernisation of the monarchy, they continue.
That would be more substantial than the "PR-led" reforms which took place after the death of Diana, Princess of Wales in 1997.
Once on the throne, Prince Charles would need to redefine the role of king because of the way he has courted controversy with his views on organic farming and architecture, says Demos.
A spokesman for the think-tank said: "It is difficult to imagine the public tolerating a king who is as personally motivated as the prince has been.
"But it is also hard to imagine Charles suddenly learning to be as impartial as his mother."
Popularity peak
Elsewhere in the essay collection, however, constitutional historian Lord St John of Fawsley argues the Queen will not abdicate.
"She is at the height of her esteem and popularity," says Lord St John.
"The only circumstances in which she would abdicated would be if she was incapable of doing her job."
The Queen's religious conviction has been one key reason cited as why she would not want to break her coronation vows.
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