Officers were called to the Tesco store in Lancaster Road, Carnforth at around 4.40am today after the break-in.
The raiders got in through the roof of the supermarket and stole an undisclosed amount of money from the ATM.
A police spokesman said a member of staff opening up the store heard noises coming from inside.
The thieves had cut through a wall to get into the cash machine.
DI Paul Richardson from Lancaster CID said: “We believe this was an organised break-in which must have involved some level of planning.
“If anyone saw anything or anyone suspicious in the area in the days leading up to the theft, please come forward and speak to us.
“Similarly, if you know anything that you think could help our investigation, please get in touch.”
Anyone with information can call us on 01524 596456 or if they fail to get an answer, 101, quoting incident reference 188 of October 5th.
Alternatively independent charity Crimestoppers can be contacted on 0800 555111 or online at crimestoppers-uk.org.