Produced and directed by Sanjay Leela Bhansali, the film starring Ranbeer Singh, Deepika Padukone and Priyanka Chopra, is scheduled to release on December 18.
As per the plea, the movie alegedly portrays their ancestors in poor light which has hurt their reputation.
"Bhansali's Bajirao Mastani venture aimed at earning profit had distorted historical facts according to the film's promos and songs," one of the four petitioners Awais Bahadur, who claimed to be heir of Peshwa Bajirao and Mastani, told reporters here.
Awais claimed that he was the member of eighth generation of Bajirao and Mastani.
Lawyer A N Shaikh said hearing before the High Court hasn't been scheduled yet.