Shivraj Chouhan took oath last month.
Congress Rajya Sabha member Vivek Tankha has written a letter to President Ram Nath Kovind, alleging that the Shivraj Singh Chouhan-led Madhya Pradesh government is "unconstitutional" as it is functioning without the council of ministers.
If Mr Chouhan is not in a position to constitute his council of ministers, "then a case of breakdown of constitutional machinery would be self-evident in the state, warranting the union to consider imposition of President's Rule in the state," he said.
Mr Tankha has urged the president to use his powers to ensure that Chief Minister Shivraj Singh Chouhan immediately forms a council of ministers, including a health minister in view of the coronavirus crisis.
Mr Chouhan took oath as chief minister for a record fourth term on March 23 after the collapse of the Kamal Nath- led government in the state. Due to the coronavirus outbreak and lockdown in the entire country, he has been unable to constitute his council of ministers.
"It is unconstitutional as there is only chief minister who is operating without a council of ministers during this exigent time of the coronavirus disease," Mr Tankha said in his letter to Kovind on Saturday.
He also accused Madhya Pradesh Governor Lalji Tandon of maintaining an "enigmatic silence despite this constitutional outrage".