West Yorkshire Police said officers arrested the 63-year-old in the Merseyside area last night and detectives are questioning him at a police station in West Yorkshire.
Mr Flowers, a Methodist minister, was suspended by both the church and the Labour party following allegations that he bought and used illegal drugs.
Mr Flowers stepped down from his role as Co-op bank chairman in June and questions have since been asked about his competence in the role.
He has also been engulfed in allegations of illegal drug use, gay sex, questions over his expenses claims at a drug charity and drink-driving.
It also emerged he had resigned as a Labour councillor in Bradford after adult material was discovered on his computer.
Co-op bank is seeking to recover contractual payments made to Mr Flowers, and he has been told to hand back £31,000.
“When Paul Flowers relinquished his responsibilities in June, it was agreed, as per his contractual obligations, that his fees for the rest of his period of office would be paid,” the bank said in a statement.
“Following recent revelations, the board stopped all payments with immediate effect and no further payments will be made.”
An “internal fact-finding review” - looking at emails and other evidence - is being carried out by the bank.
The assistant secretary of the Methodist Conference, the Rev Gareth Powell, acknowledged the risk that allegations against Mr Flowers would “tarnish” the church’s reputation.
Mr Powell told the BBC: “I think inevitably some of the speculation has raised questions, as it always does for the church, about the trustworthiness of ministers.
“Inevitably, it’s regrettable when the allegations made against one minister then tarnishes the extremely good and honourable work undertaken by all of our ministers.
“Certainly the actions that are now under public scrutiny inevitably raise a question about the role of the church.”
It was reported today that Mr Flowers was the subject of an inquiry into “lavish” expenses claims at the Co-op when he resigned from the mutual’s group board in June. The BBC said he stepped down after being confronted with a dossier of his claims, compiled by the then-chairman Len Wardle.
He quit as chairman of the Co-op Bank at the same time after the group brought in banking industry veteran Richard Pym to replace him.
Mr Powell told BBC Radio 4’s Today programme that the Methodist Church dealt “appropriately” with Mr Flowers’ historic convictions for indecency and drink-driving, but said the church was not informed of other concerns now being raised by different organisations.
“I don’t think we were incurious,” said Mr Powell. “The necessary processes that dealt with the two convictions had reassured themselves that here was a person who could continue with our ministry like any other Methodist minister under the normal discipline of our ministry.
“I don’t think it was being incurious. There is a fine balance to strike between curiosity on the basis of evidence presented and curiosity based on speculation and gossip.”
Mr Powell said that the church was given “no formal indication” by Methodist ministers of concerns about inappropriate behaviour by Mr Flowers.
He added: “People make observations about those who are in the public eye, but we are not able to act on comments about a person’s behaviour without any firm evidence.
“Clearly, it would have been immensely helpful to us if bodies had been rather clearer about some of the concerns in the past. Hitherto, we have dealt appropriately with what we have known about in a formal context.”
A Conservative member of Bradford Council, John Pennington, said he and other councillors were told that Mr Flowers was leaving the authority due to work pressures, and not as a result of pornography being found on his computer.
Mr Pennington told the programme: “We were told he had resigned through pressure of other work commitments - ie, the Co-op Bank.
“He was a very believable, very plausible chap, always immaculately dressed. He speaks with confidence and even with an air of superiority. On the surface, a hail-fellow-well-met and seemingly well-connected.
“To be frank, I’m not surprised that he has worked his way up the greasy pole because he is very, very plausible. What does concern me is the seeming lack of any checks or any vetting procedure to stop him getting to the dizzy height that he got to.”