An Air India official told the BBC that the order had been made on the basis of a document issued by the civil aviation authority last year.
The airline had warned 600 of its crew to "shape up" last year, but 125 had not managed to maintain the required weight, the official said.
The airline says however that the issue is not one of weight, but "fitness".
Airline officials confirmed to the BBC that the directive had been issued, but said it was part of an internal document which they could not comment on publicly.
They said the basis for the recommendation was concern that "unfit" cabin crew would not be able to operate efficiently in emergency situations.
Aviation regulations state that a Body Mass Index (BMI) of 18-25 is normal for a male cabin crew member, while for a female it is 18-22.
Aviation expert Kapil Kaul told the BBC: "An overweight crew is a signal the airline is not fit. You need a smart friendly agile crew that can complement the image of the airline."
Air India to ground 'fat' cabin crew