Three vehicles, a dark-coloured estate car, a silver Ford Transit Van, and a dark-coloured Land Rover display were involved in the raid which took place at about 2.45am today (January 19).
Thieves smashed the front glass window of the store, and using the discovery, ripped the cash machine from inside and into the main car park where it was lifted into the Ford Transit van.
All vehicles then left the scene and drove along the A429 towards Cirencester. The Land Rover Discovery which was stolen has since been recovered.
Detective Constable Jo Chesshire from Chippenham Tasking Team, said: "We believe six or seven men were involved in this incident - it is not clear at this stage how much money was inside the ATM, but a significant amount of damage was caused to the front shop.
"We've been carrying out extensive enquiries today in relation to this incident and we would be keen to hear from anyone who may have seen or heard any suspicious activity or any vehicles in the area of the A429 between 2am and 3am who may have dash cam footage featuring vehicles including 4x4s, estates or vans that were travelling in convoy."
Anyone with information should call police on 101 or Crimestoppers anonymously on 0800 555 111.