Desai, a former MCI chief, was arrested on charges of bribery in 2010.
Senior lawyer and Aam Aadmi Party leader Prashant Bhushan told media that several political parties pushed for Desai's reappointment to his post in MCI.
He said the political parties set aside their ideological differences, despite the criminal cases against Desai.
Desiraju "was unfairly and arbitrarily transferred" by Health Minister Ghulam Nabi Azad as Desiraju was against the return of Desai to the helm of the MCI, the AAP said in a statement.
Desiraju was moved to the department of consumer affairs. Lov Verma, secretary in the department of AIDS control, has been given the additional charge as health secretary.
AAP quoted Desiraju as saying in an internal health ministry note: "It is widely believed that all decisions within the MCI are being taken by (a) group led by Ketan Desai."
"There is every likelihood that we will be forced to approve and notify decisions regarding courses, new admissions... which have been made on grounds other than merit."
The AAP release said "the honest and upright (Desiraju) has been removed because of his sincere efforts...."
"In October 2013, the Gujarat University, at the behest of Modi's government, nominated Desai as a member of the MCI despite two cases pending against him in the court of law," the statement said.
The statement further claimed that Samajwadi Party chief Mulayam Singh Yadav had requested Dec 9, 2013 to the prime minister to notify him so that he may participate in the general body meeting of MCI on the very next date.
At a function here Friday, Health Minister Azad refused to comment on the AAP charges.