The incident happened around 2am on Sunday, August 30, local officers alerted after the occupant of the property noticed the device had been taken.
Inquiries are ongoing to trace those responsible. Anyone who can assist officers with their investigation is asked to come forward.
Inspector Keith Dougal said: “This defibrillator is valued at around £1,000 but more importantly, it is a vital piece of medical equipment for the village.
“We are keen to speak to anyone who remembers seeing any suspicious activity around Lammermuir Cottages on the evening of Saturday, August 29, or the early morning of Sunday.
“In addition, anyone with any further information relevant to our inquiry should also contact police immediately.”
The Juiced Up music festival was on in Cranshaws over the weekend and afterwards one of the organisers said: “We were informed that a witness had seen some people around the area of the equipment at 1.30am.
“We are working with Police Scotland to locate the people responsible for the theft should they have come from our event. I will be going to Cranshaws at the weekend to speak with the residents of the village to see if Juiced Up can help in any way.”
“People are shocked that such a cynical and heartless crime should have happened, but hugely relieved that the loss was discovered by a local resident not someone in need of a defibrillator,” said Mark Rowley, chairman of Lammermuir Community Council.
“We bought three defibrillators for our community council area from our own community’s funds after the Scottish Ambulance Service told us that chances of surviving cardiac arrest decrease by 10% for each minute before resuscitation!
“With the nearest ambulance 18 minutes away and out-of-hours medical cover now all at BGH it became an instant priority to help protect our own communities and the many walkers, cyclists, anglers and visitors that use the area.
Those with information can contact Police Scotland on 101 or alternatively, the charity Crimestoppers on 0800 555 111.