The store on Glenesk Road in Langholm was broken into at about 02:35.
It follows similar incidents last month at a Co-op petrol station in Lockerbie and a supermarket in Moffat.
Police are gathering and studying CCTV footage in an effort to identify and apprehend the people responsible for the latest break-in.
Det Insp Scott Young said: "I would urge anyone who saw anybody acting suspiciously in the area to come forward to police as a matter of urgency.
"In particular I would like to trace two men who were seen in the Waverley Road area around 11.30pm on Wednesday evening.
"They were wearing dark coloured clothing and baseball caps."
Police are want information on two vehicles seen between 23:30 on Wednesday and 03:00 on Thursday.
One was a light coloured Transit-type van and the other was a small white hatchback car.
"The police investigation is continuing into similar incidents at the Co-op petrol station in Lockerbie and the Co-op in Moffat last month," added Det Insp Young.
"We believe that these previous incidents are linked to this break-in."
Police believe a cigarette raid at a supermarket in southern Scotland is linked to two previous incidents at Co-op premises.