Lawnmowers, a scarifier and a turfer were taken from the Lockerbie site some time between 09:00 on Thursday and the same time on Friday.
Det Con Scott Barr said it appeared to have been a "targeted raid" with a vehicle needed to remove the property.
He appealed for anyone who may have seen anything suspicious in the area to contact them as soon as possible.
Grass cutting equipment worth about £20,000 has been stolen from a south of Scotland bowling club.