Murshidabad Deputy Superintendent of Police Soumayajit Baruah said the clash erupted over the possession of a party office at Uttarpara area here.
The two sides clashed with sticks and iron rods and the situation was brought under control by the police, who rushed to the spot.
Later RAF was deployed in the area to prevent outbreak of fresh clashes and to maintain peace, Baruah said.
The injured included a security person of Congress Zilla Sabhadipati Shiladitya Haldar, he added.
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He alleged that this morning the TMC workers descended at the party office armed with sticks and iron rods and the two parties clashed.
TMC district president Mannan Hussain when contacted said the clash was not directed by TMC.
"All the Congress leaders who had started the party's office and used to sit there had in fact switched over to TMC," he added.