Raiders took the machine from inside a branch of Nat West, in Main Street, Heslington, near York at about 02:30 BST .
North Yorkshire Police said the machine was loaded on to a truck and driven away before the thieves escaped in a black Jaguar.
The digger, which was reported stolen on Wednesday, was left at the scene.
A force spokesman said "extensive enquiries" are ongoing and  appealed for witnesses to the raid to come forward.
Thieves used a stolen digger to smash through a bank wall and steal a cash machine.