The industrial vibrating plate, known as a wacker plate, was taken from Samye Ling overnight on Sunday to Monday.
It weighs about 160 kilograms and police say it would require a vehicle to remove it.
Constable James Wishart, of Police Scotland at Lockerbie, said “This is yet another high value theft in a very rural part of our region. We are again reminding the public to be vigilant to any suspicious activity in their community and to report it immediately through our 101 number.
Meanwhile, also last weekend – between Friday to Monday – a forestry shed at Garwaldfootwater, also Eskdalemuir, was broken into. However, officers say nothing appears to have been stolen there.