The incident happened at around 1.40am outside the Heron Foods store on Cockerton Green.
It is believed the suspects have filled the free-standing machine with gas, which has then been deliberately ignited, before making off with an unknown quantity of cash.
Detective Inspector Sharon Alderson, from Durham Constabulary, said: “Nobody was injured during the incident. However, it has caused significant damage to the cash machine.
“A cordon remained in place this morning while we conducted our enquiries.”
She added: “In October last year, a cash machine on Neasham Road was targeted in a similar way.
“Enquiries are ongoing to determine if the two incidents are linked.
“We would like to appeal to anyone who may have seen or heard anything in the Cockerton area of Darlington in the early hours of Wednesday 14th to come forward.”
It is understood that a car was seen leaving the scene at the time of the incident.
Anyone with information should call Durham Constabulary on 101, quoting incident number 24 of February 14th.
Alternatively, pass on to Crimestoppers anonymously on 0800 555 111.
