Former chairman Paul Flowers, a 63-year-old Methodist minister, was filmed talking about buying crystal meth, crack cocaine and ketamine by the Mail on Sunday tabloid newspaper in allegations published last weekend.
Flowers, also a former local councillor for the opposition Labour party, has since apologised - leading to his subsequent suspension from the church and Labour.
A police statement released Saturday said officers had last day "arrested a 63-year-old man... in connection with an ongoing drug supply investigation".
Reverend Flowers was chairman of the Co-operative Bank which prides itself on ethical investments - from 2010 until June earlier this year.
The lender and financial regulators are currently facing serious questions over his appointment, especially in light of the fact that the Co-op finds itself in a troubled financial state.
Conservative Prime Minister David Cameron on Friday said that he would order a formal inquiry into the finances of the bank, which faces a big recapitalisation to cover bad loans and the costs of a failed expansion plan.
Flowers has meanwhile been engulfed in a highly damaging series of allegations over illegal drug use, sex with rent boys, drink-driving and questions over his expense claims while working for a drugs charity.
The allegations and the arrest of Flowers further damages the reputation of the Co-op just weeks after it unveiled a drastic restructuring that will hand control to US hedge funds in order to plug a 1.5-billion pounds hole.
The revelations have sparked also the resignation of Len Wardle, who has stepped down as chairman of parent firm the Co-operative Group and who led the board that appointed Flowers three years ago.
The BBC Saturday reported that Flowers - who was paid 132,000 pounds a year - resigned from the Co-op in June after being confronted by "lavish" expense claims, and growing doubts over his competence.
The Co-op Bank has meanwhile said that it is seeking to recover contractual payments made to Flowers, and he has been told to hand back 31,000 pounds.