In December, Khobragade, 39, ran afoul of U.S. law in an employment case involving a domestic household servant.
The Hindustan Times reported she left the United States under full protection of diplomatic immunity Thursday morning. Federal prosecutors charged her with visa fraud and making a false statement in an indictment handed up by a federal grand jury in Manhattan.
The indictment alleged Khobragade and others tried to "silence and intimidate" the household worker and her family members.
Her arrest and strip-search Dec. 12 strained U.S.-India relations and triggered protests in India. She would face the charges if and when she returns to the United States.
The New York Times reported the decision by U.S. Attorney Preet Bharara to seek the indictment likely would continue to strain diplomatic relations between the two countries.