It happened at a Co-operative Bank cashpoint outside the Matalan outlet on Neasham Road, Darlington, at around 1.20am.
Debris, including anti-ram raid bollards, was sent flying across the car park as the blast destroyed the kiosk.
Acting Inspector John Hoar, from Durham Constabulary, said: "The suspects have used an explosive device causing significant damage to the cash machine.
"It is not yet known if the suspects managed to get away with any cash as investigations are in the early stages."
Police swiftly reassured people overnight that the explosion was not terror-related.
Detectives think a car sped away from the scene and they appealed for witnesses to ring 101.
Locals reported feeling the blast "over two miles away".
Resident Harry Chown, 28, told the Press Association that he was woken at around 1am by a "violent explosion which shook my house".
He added: "It looks like thieves have gone overkill on explosives whilst trying to blow open a standalone ATM.
"It's been obliterated and flattened trees and signs and scattered debris everywhere. Social media suggests people two miles away heard it which explains why my house shook so violently only 150m away."
Mr Chown said the explosion had "shoved" the kiosk containing the ATM "10 metres along the carpark".
Locals wrote on social media that they had felt the blast at the store, which is close to the town's train station.
Kerry Moor wrote on Facebook that she was "over two miles away and our house shook", while James Cummings said: "I live directly across from there and was awake at the time and the shock of the explosion shook my house and knocked me out of my bed."
Neighbourhood Inspector Chris Knox said police believed the thieves got away with an unspecified amount of cash, but that was not yet confirmed.
The raiders may have miscalculated the amount of explosive material needed, and it was possible one of them may have been injured, he said.
Inspector Knox told a news conference at the scene: "The explosion was heard over a large area in Darlington and people did turn up at the scene from across the town due to the noise it generated."