The shutters of the supermarket on The Strand were forced and the intruders, who tried unsuccessfully to remove the ATM with the help of a van, made off with a quantity of cigarettes.
A spokesperson for The Co-operative said: "Intruders attempted, but failed, to remove the store's ATM, then entered the building and stole a small quantity of cigarettes.
"No staff were in store at the time. The front door suffered some damage, but the store's ATM was undamaged. The front door was swiftly fixed and the store opened and traded as normal.
"CCTV footage has been given to the police who are investigating and, as with any incident such as this, we would appeal for anyone with information to come forward."
Detective Constable Clarke, from St Ives police, said that the raid was being linked to a second incident in St Ives during which a quantity of cigarettes was taken from a shop.
Two men, aged 38 and 22, were later arrested in the Lelant area. They were questioned and have now been released on police bail pending further inquiries.
article copyright THE CORNISHMAN