An explosion was used to break into a cash machine in Kirkby Stephen.
Police say the raid was carried out by a group of men in a white van.
It happened at the Co-op in North Road in the early hours of Saturday.
The ATM machine was badly damaged, and cash stolen from inside.
Police said the men had used a "dangerous and unpredictable technique" to carry out an explosion and gain access to the store.
Nobody was hurt and officers have stressed that this type of crime is rare in Cumbria.
They say some of the stolen money will have been damaged by the explosion.
Shopkeepers and business staff are being asked to look out for notes that are scorched or damaged.
People are also being urged not to approach a cash machine if they have any suspicion that it is being tampered with in this way.
Instead they should keep their distance and call 999.
Detective Sergeant Matthew Belshaw said: “The offenders have employed a dangerous and unpredictable technique that involves first pumping gas into the front of the ATM, via a canister, before igniting the gas and causing an explosion.
“This technique is not only extremely dangerous to the criminals employing it but also to any members of the public who may be nearby, or unsuspecting workers who may be present within the targeted establishments.
“Fortunately on this occasion no one was hurt or injured, and these crimes are still rare."
He added: “This incident has been opportunistic and has taken place when the store has been empty and at a time when there has been no one around.
“It is known, due to the heat of the explosion, some of the stolen money is damaged. Cumbria Police are asking all shopkeepers and establishments to be conscious of receiving any money that is scorched or damaged and to make contact if they have.”
Forensic investigations are underway, and Cumbria Police are also working with other forces to trace the thieves.
Police are appealing to any witnesses to come forward.
Similar offences across the country have involved the offenders hiding their gas canisters nearby in preparation, before disposing of them nearby afterwards.
Anyone who witnesses any suspicious activity should call police on 101, or 999 in an emergency.
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