Investigators say the theft in Moffat in Dumfries and Galloway would have required careful planning as the animals were on grazing land covering thousands of acres.
The stolen Cheviot sheep are worth an estimated £60,000.
Police want to speak to anyone who saw anything suspicious in the 24 hours after 5pm on Sunday.
Detective Inspector Scott Young said: “The theft of such a large amount of sheep would have required careful planning and obviously there must have been vehicles used.
“The grazing land the sheep were on covers several thousand acres north of the A708 Moffat to Selkirk road near to Greymares Tail in Moffat.
“I would urge anyone who saw anybody acting suspiciously in this area between the times stated, or anyone with information that may assist our police investigation to contact Dumfries police office.”