Officers arrested the three men and one woman on Wednesday during a series of raids in the Bradford, Darlington and Middlesbrough areas.
Also in crime: Woman attacked with meat cleavers outside her shop in LeedsCash machines were targeted across both regions between October 26, 2017 and February 14 this year.
More than £300,000 was stolen, while thousands of pounds worth of damage was caused to nearby buildings and businesses.
Detective Inspector Lee Fletcher, of the Yorkshire and Humber Regional Organised Crime Unit, said: “Cash machines can be a vital local resource to people – especially in more rural areas. People can rely on them as a nearby supply of available cash.
“But it can take up to seven months for a damaged or stolen machine to be replaced – so the entire community can be the victim with the next nearest ATM could be many miles away.
“Increasingly dangerous tactics are being used by some criminals who are trying to take ATMs. We are working closely with police forces, local communities and the ATM industry to prevent and detect such offences.
“We need people to report any suspicious activity they see to us. Even if it turns out to be incorrect information or it doesn’t lead anywhere it can help us to build up a more complete intelligence picture.
“One call could make all the difference.”
Also in crime: The 19 alleged Class A drug dealers charged with operating in Leeds city centreThe three men questioned by police were a 34-year-old arrested in Bradford, a 34-year-old arrested in Darlington and a 45-year-old arrested in Middlesbrough.
They were arrested on suspicion of conspiracy to cause an explosion, conspiracy to commit burglary, conspiracy to commit theft and conspiracy to enter into or be concerned in the acquisition, retention, use or control of criminal property.
A 45-year-old woman was arrested in Middlesbrough on suspicion of conspiracy to enter into or be concerned in the acquisition, retention, use or control of criminal property.
Vehicles and cash were also seized during the operation.
All of those arrested have been released under investigation, police said.