The latest incident happened in the Market Square area of Bushmills in Co Antrim.
It is understood to be ninth such attack in the Province this year, and police have previously said they believe several criminal gangs could be responsible.
Detectives are asking anyone who saw a digger being transported on the roads in the area, or anyone who witnessed the incident, to contact them on the non-emergency number 101.
TUV leader Jim Allister said he was “angry and disappointed”, adding that the theft represented the loss of a “vital service” for Bushmills.
The North Antrim MLA continued: “The paucity of policing in North Antrim is, I believe, making life easy for the criminals. With barely a police officer or police vehicle available within north Antrim during the night, with such service as there is withdrawn to Coleraine, the area has been left wide open for these gangs, who are not ignorant of the opportunities lack of policing presents.”
Mr Allister said that, following the previous theft of an ATM in Ahoghill, he expected an increase in surveillance and patrols by the PSNI.
“But once more the criminals are winning,” he added. “This is not good enough.”
TUV candidate in Bushmills, Cyril Quigg said: “The derelict police station in our Main Street is an advert to the criminals of how easy crime has become. With a theft like this fine tuned to three or four minutes, waiting for police to come from Coleraine means the criminals are long gone.
“The local community is being let down badly by an over centralised policing policy. Meanwhile, the criminals are laughing all the way to their next heist.”
Retail NI Chief Executive Glyn Roberts branded the theft a “shameless attack on a rural town which was preparing for a busy Easter weekend of visitors and tourists”.
He added: “The loss of this ATM means that the local community and tourists will be restricted in accessing cash.
“Every single ATM robbery brings rural Northern Ireland that much closer to being a cash-free zone. Regardless if whether have been robbed, many Retail NI members are now considering removing their ATMs for fear of their shops being smashed up.
“Retail NI will be meeting the Policing Board on Thursday to discuss the police response and what more can be done to tackle this crisis.”