The Times of India reported that crew members threw punches and hurled abuse at each other on the flight from Sharjah in the United Arab Emirates to Delhi after a female attendant accused the pilots of sexually harassing her.
The fight spilled out into the galley of the plane as about 100 passengers looked on, the paper said under the headline "Pilots, crew slug it out at 30,000 feet".
The cockpit of the Airbus A-320 was left unmanned at one point, and one of the pilots threatened to divert the plane to Pakistan, the Times alleged.
The 24-year-old female crew member and a co-pilot both suffered bruises in the incident on Saturday and police have registered a case against the pilots for "outraging the modesty of a woman," it said
"There are several eyewitnesses and we are recording their statements," the Times quoted police commissioner Satyendra Garg as saying.
State-run Air India said in a statement it had ordered an inquiry into what it described as a reported "scuffle",