The fracas took place Thursday afternoon when the gates of the Anjuman-e-Islam school, which had been locked during filming, were opened to let parents pick up their children.
M.H. Belose, additional chief metropolitan magistrate, later Friday freed the three bodyguards on bail and asked them not to leave the country for one week. They deposited bail guarantees for $545 each.
Belose also asked the three to report to local police every day for one week.
Witnesses said Jolie's bodyguards pushed and shoved some of the parents. Police prosecutor N.C. Tambe told the court that the three had upset people by calling them "bloody Indians" and "bloody Muslims."
If convicted, the three can be jailed for up to three years.
Mahesh Jethmalani, attorney for the British bodyguards, said there was no reason for police to arrest them.
"They have come to India to shoot a film," Jethmalani told the court, denying claims they were abusive.
Police identified the bodyguards as Thomas McAdam, 47, Robert Dunn, 35, and Michael Brett, 50.
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 the 31-year-old actress.
It was the latest in a string of confrontations that Jolie's bodyguards have been involved in since the Hollywood star arrived in India last month to film scenes for the movie about slain American journalist Daniel Pearl.
"A Mighty Heart" is based on a memoir written by Pearl's widow, Mariane. Pearl, who worked for The Wall Street Journal, was abducted and murdered in Pakistan in 2002 while researching a story on Islamic militancy.