It is thought that four men, who were drinking in the pub, smashed the front of the machine and stole the cash box. They then left the pub and may have left the area in a dark coloured car.
Anyone with any information is asked to call Lincolnshire Police via the non emergency 101 number, or call independent charity Crimestoppers anonymously on 0800 555 111.
Cllr. Giles McNeill, Conservative (Nettleham Ward), said:
"This is a very serious crime and I hope that we can expect a proper investigation by local police. Obviously if any one has any information I encourage them to contact the police or Crimestoppers.
"I can only imagine how distressing this is for the pub's landlord and local residents. I urge people to be vigilant in the future."