The suspects arrived outside the Co-op in Oldham Road in a dark grey Land Rover Defender at around 3.45am. They damaged the door to the ATM cash machine and attempted to steal money from inside.
The raid was unsuccessful however and they drove away in the Land Rover towards the motorway without taking any cash from the machine.
West Yorkshire Police has asked witnesses to come forward and said they particularly wanted to speak to the occupants of three white vans that were parked in the Co-op car park at 3am and left the scene several minutes before the incident.
Anyone with any information is asked to contact Halifax CID via 101 quoting crime reference number 13180145613. Alternatively, call independent charity Crimestoppers anonymously on 0800 555 111.