The fracas broke out when the Left Front moved an adjournment motion over the state government's alleged failure to curb chit funds in the state.
After Assembly Speaker Biman Banerjee rejected the plea for an adjournment motion, lawmakers from the two sides came to blows. Following the scuffle, the house was adjourned.
Three Left legislators - Amjad Hussain, Nazibul Haq and Sushanta Besra - have been suspended by the speaker for the day.
Both the Congress and the Left Front walked out of the house in protest.
"Time and again we have been denied our demand of admitting an adjournment motion on important issues involving public importance. Since the Trinamool government has come to power all our adjournment motions have been rejected for discussion, mostly on flimsy grounds," Leader of Opposition and Communist Party of India-Marxist (CPI-M) politburo member Surjya Kanta Mishra said.
Mishra said his party member Gouranga Chattopadhyay had to be hospitalised after being assaulted allegedly by Trinamool members in the assembly.
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"Not only Chattopadhyay was assaulted but also our women legislator Debolina Hembram was manhandled and filthy language was used against her," said Mishra.
The Left Front has called the suspension of its members as "unconstitutional" and has sat on a demonstration outside the assembly, demanding their suspension be revoked.
"The suspension of three of our members is against the principles of natural justice and the constitution because they have not been given an opportunity to be heard. They have been punished without being able to defend themselves," Mishra said.
"The decision of the speaker to suspend our members was influenced by the minister of parliamentary affairs (Partha Chatterjee), which is unacceptable and goes against the law of the land. We will continue to protest until their suspensions are revoked," added Mishra.
"Some of our members were crying. We all were apprehensive of our security, we have walked out for the day. It is really surprising that the temple of democracy has been polluted and desecrated," Congress leader Manas Bhunia said.