Bandyopadhyay was earlier arrested by the Central Bureau of Investigation in connection with the Rose Valley Chit Fund scam.
Banerjee demanded the arrest of Prime Minister Narendra Modi and BJP President Amit Shah instead.
"We strongly condemn the politically vindictive attitude of Modi and Amit Shah. They have arrested our Parliamentary Party leader Sudip Bandyopadhyay. He is a veteran politician and senior leader of our party.
"It is all because of our fight against NoteBandi (note ban). We are and will be with the people. Nothing can stop us from being with the people and we will continue with our protest against NoteBandi," she added.
"We condemn, condemn and condemn this," she said in a Facebook post.
Banerjee said her party will launch pan-India protests against the Centre's vindictive attitude.
"We will hold a demonstration in front of Kolkata RBI on January 9 and there will be dharnas in 10 different states including Delhi, Assam, Odisha and Tripura on January 10 and 11," she said.
"I also run a government and I also have the power to arrest certain people who are thieves, hooligans and extortionists. This arrest has been made under pressure from the PMO.
"This is vendetta politics because the Trinamool is fighting against the Centre over demonetisation," she told the media earlier.