CPI-M leader Surya Kanta Mishra accused Trinamool Congress legislator Arabul Islam of leading the attack in South 24 Parganas' Bhangar area.
"(They) assaulted Molla when he went to Bhangar to visit our party office, which was set on fire by Trinamool workers last night," Mishra said.
"Molla got multiple injuries on his mouth and waist. He has been admitted to a hospital in Kolkata," said the Communist Party of India-Marxist leader.
He demanded the arrest of Islam and others. Hospital sources said Molla's lower lip had been stitched and his condition was now stable.
State Congress chief Pradip Bhattacharya condemned the incident and also demanded the arrest of the Trinamool legislator.
Islam rejected the accusation and alleged that Molla was making a "false statement" to malign the Trinamool Congress.