The Rapid Action Force (RAF) had to be called in to maintain peace in the area, they said.
The two parties traded allegations over the incident that took place in Kantaberia near Uluberia, ahead of a BJP roadshow for the upcoming Uluberia Lok Sabha by-election, a police officer said.
BJP supporters claimed that two of their members were injured when TMC workers attacked them in Kantaberia shortly before the start of the roadshow in Gangarampur here, he said.
On the other hand, TMC supporters said the party's banners were set on fire by the BJP workers, who also allegedly disfigured posters of Chief Minister Mamata Banerjee, police said.
"Atrocities have become widespread in West Bengal, and this incident is no exception. The CM (Mamata Banerjee) is responsible for all this," BJP leader Mukul Roy said after the roadshow.
Countering him, TMC Howrah district head and MLA Pulak Roy said that BJP is concerned about "losing its deposits" before the by-elections, and are trying to "disrupt peace" in the area.
One person has been detained for questioning in connection with the incident, the police officer said, adding, the situation was under control at present.