The fracas began when the gates of the Anjuman-e-Islam school, which had been locked during filming, were opened to let the parents fetch their children.
"This Jolie's bodyguard called one parent, `You bloody Indian,"' said Mohammed Yusuf Patni, general secretary of the school's Parent Teacher Association. "Children were pushed around."
Patni, who has two children studying at the Muslim school, said "mothers were also shoved aside by the guards."
Dallington TV, a British production company that organized the shoot, blamed the scuffle on photographers and television cameramen that it said rushed the school to get pictures of Jolie.
"We had the full permission and cooperation of the school to film on the premises," Dallington said in a statement. "When the gates were opened to allow the parents in to collect their children, the paparazzi rushed the school causing confusion."
Representatives for Jolie refused to comment.
The scuffle wasn't the first that security guards have had since Jolie arrived in India last month with Brad Pitt and their three children.
In one incident, an Associated Press freelance photographer alleged that security guards protecting Jolie's movie set in Pune had hit him and threatened him with a gun.
Earlier, as Pitt and Jolie were leaving a hotel, one of their security guards manhandled a British photographer trying to take their photo, grabbing the man by his neck and verbally abusing him.
"A Mighty Heart" is based on a memoir written by Mariane Pearl, the widow of Daniel Pearl, a reporter for The Wall Street Journal, who was abducted and murdered in Pakistan in 2002 while researching a story on Islamic militancy.
Jolie had said that playing Mariane Pearl is "certainly challenging for me, as I have to make the world understand this woman and her family."
"She still loves Pakistan, she carries no hatred. She is above all that, and her strength is a reminder that this is what the world needs," the DNA newspaper quoted Jolie as saying.
Directed by Michael Winterbottom, "A Mighty Heart" is expected to be released next year.