According to the police, the arrests were made after Prof Ambikesh Mohapatra lodged a complaint that he was assaulted by a group of about 15 people on Thursday night for posting the cartoons.
The four arrested persons were identified as Amit Sardar, Arup Mukherjee, Sk Mustafa and Nishikanta Ghorai. Two of them were allegedly Trinamool Congress workers.
All the four, however, were given bail on personal security bonds of Rs500 each by the Alipore court where they were produced.
Prof Mohapatra and his neighbour Subrata Sengupta were arrested on Friday for posting a cartoon on a social networking site featuring Banerjee with Railway Minister Mukul Roy and his predecessor Dinesh Trivedi.
The cartoon showed the chief minister and the railway minister exchanging dialogues from a popular Bengali film by Satyajit Ray which alluded to the replacement of Dinesh Trivedi by Mukul Roy as railway minister.