Complainant Kripesh Tripathi claimed that the statement has hurt the sentiments of followers of Swami Vivekananda as well as the general public.
Such comments also pose a threat to the unity and integrity of the country, he claimed.
The complaint goes on to question as to how could the BJP president have known about the IQ levels of the two individuals.
Gadkari's speech in Bhopal on Sunday, which appeared to compare the Intelligence Quotient of Swami Vivekananda and Ibrahim, has already come under attack from his political rivals.
The next hearing for the case has been scheduled for November 23.