The wheelchair-bound athlete, Deepa Malik, who won a silver medal for India at 2016 Paralympics in Rio, complained of rude behaviour by a cabin crew member of the TATA-SIA-run Vistara.
However, the airline subsequently issued an apology.
The first Indian woman to win a medal in Paralympic Games, Malik was travelling on Vistara's Mumbai-Delhi flight UK 902 on Wednesday, when the incident happened.
The 46-year-old complained about the "poor handling" of wheelchair-bound passengers by the airline staff.
According to her complaint, a crew member Priyanka was very rude in the flight as she asked her to speak softly when she called parents to inform them about the delay in flight.
"On objecting, she said 'sweetheart, chill'," Malik wrote, adding that the airline's wheelchair handling was so poor that they didn't know how to shift a person from the seat to cabin chair.
She alleged that the cabin crew was not ready to help her reach the cabin seat, as they were not trained.
In a series of tweets, she also tagged Union Social Justice and Empowerment Minister Thaawar Chand Gehlot.
Acting on her complaint, Vistara apologised to her publicly on the social media.
The airline also assured her of a through probe into the incident and necessary action.