Professor Ambikesh Mahapatra teaches chemistry at Jadavpur University. A court released him on bail.
Police say he forwarded doctored images of Ms Banerjee, former Railway Minister Dinesh Trivedi, whom she recently sacked, and his replacement Mukul Roy.
The cartoon went viral on the social networking site Facebook.
Prof Mahapatra was arrested for “spreading derogatory messages against respectable people”, said Sujoy Chanda, Deputy Commissioner of Calcutta police.
Ms Banerjee took over West Bengal last year after 34 years of Communist government
The professor has been charged under India’s information technology (IT) Act.
His fellow professors and intellectuals have condemned his arrest, calling it an attack on free speech.
The chief minister, who came to power in 2011 bringing to an end the state’s 34-year-old Communist rule, has recently attracted a lot of negative publicity.
The government’s recent order to paint Calcutta blue was criticised by many.
Many of Ms Banerjee’s high-profile supporters, including party MP and singer Kabir Suman, theatre actor Kaushik Sen and educator Sunanda Sanyal, have also begun criticising her government