The move by the legislators came soon after Jyotiraditya Scindia's resignation from the Congress.
Congress MLA Bisahulal Sahu, who resigned from the Assembly and joined the BJP on Tuesday, said that many more Congress MLAs would leave the party as they are unhappy with party leadership.
After joining the BJP in the presence of former Madhya Pradesh Chief Minister Shivraj Singh Chouhan in Bhopal, Mr Sahu said, "I have resigned from the Congress as well as from the membership of state Assembly."
"I have joined BJP. Most of the Congress MLAs will resign from the party in the coming days as they are unhappy with the functioning of the Kamal Nath government," he said while speaking to media.
Besides Mr Sahu, 19 Madhya Pradesh Congress MLAs, including six state ministers, too tendered their resignation from the Assembly on Tuesday.
The move by the legislators came soon after Jyotiraditya Scindia's resignation from the Congress.
Congress has been witnessing an internal turf war in Madhya Pradesh since the party formed a government in the state.