Officers were called to the Co-op on Loxley Close at around 2.15am this morning (Saturday 22 December) after alarms were set off.
A cash machine is understood to have been removed from the store before being loaded onto a flat bed-type vehicle, which is thought to have left the scene.
Following an area search, the ATM was located and two men - a 22-year-old man from West Bromwich and a 34-year-old man from Walsall - were arrested in connection with the incident.
They have been released on bail until mid-january.
Detective Sergeant Gareth Unett said: "Fortunately no one was injured as a result, but we would like to speak to anyone who may have witnessed the incident, seen the flat-bed type vehicle in the area or any suspicious activity earlier in the evening.
"Enquiries are currently under way but any information, no matter how small, could be key to the ongoing investigation so please get in touch."
Anyone with any information should call Warwickshire Police on 101 or Crimestoppers anonymously on 0800 555 111 quoting incident number 55 of 22 December.