Meena was director, central vigilance office, Union ministry of health.
"How can an IPS officer who has no medical education and minimum knowledge or experience in the field of medical education and research run such an important body?" a former executive member of the council from West Bengal asked.
MCI sources said Meena replaced Sanjay Sreevastava, who had resigned last week.
In 2010, the MCI was dissolved after corruption allegations surfaced, and the Union health ministry created the post of secretary.