The cash machine, outside Barclays Bank in the Market Place in Chippenham, was struck "almost 50 times" by a woman shortly after midnight on 2 July.
Officers said the woman stood at the cash machine for several minutes before removing her shoe and striking it.
Both keypad and screen were damaged in the attack. Police are appealing for help to identify the woman.
Wiltshire Police released CCTV footage of the incident on Wednesday.
A force spokesman said the reason for the attack was unknown, adding officers did not find the woman's card inside the machine.
Det Con Richard Gardner said: "This was a completely senseless and inane act which caused sufficient damage to make the machine unusable for other customers.
"I would like to hear from anyone who recognises the woman shown in the CCTV or who has any information in relation to this incident."