CCTV footage shows the man and woman walk up to the ivory and brass-plated device, worth many thousands of pounds, and unscrew it from the wall of Fairfax House in York.
The man is then seen stuffing the barometer beneath his overcoat and the couple walk out.
Museum director Peter Brown described the theft as 'audacious' and added: 'The sad thing is they are preventing hundreds of people the chance to see an extremely important part of the city's history.'
It is part of the museum's famous Noel Terry Collection of Georgian furniture and, in Mr Brown's estimation, probably unique.
'It is a huge regret for us that it is gone,' he said. 'It is an irreplaceable piece dating back to 1695. We are just trying to remain calm and hope we get it back.
He refused to confirm the exact value of the piece beyond saying it was 'extremely valuable' and worth tens of thousands of pounds.
Staff at the museum - based in a 1762 building that has been described as 'the finest Georgian townhouse in England' - noticed the barometer was missing on Tuesday morning after the couple struck at about 2.45pm the previous day.
Fairfax House's insurers are offering a reward for information leading to the return of the stolen treasure.
Mark Dalrymple, from insurers Axa Art, said: 'This seems an extremely well-planned theft. I have no doubt that the pair have been to the museum on a number of occasions planning the theft.
The woman was also white, with light brown hair, wearing a tan-coloured coat, blue jeans and carrying a satchel.
"The Fairfax Daniel Quare £500,000 Barometer stands above the Newby table"