Rajya Sabha MP Dola Sen had booked three tickets for the Air India flight, an airline official said.
The plane was scheduled for take off at 2.25 pm but could only depart at 3.04 pm. It landed in Kolkata at 4.35 pm.
Air India also alleged that on landing in Kolkata, Sen asked the officials of the local airport to get a written statement from all passengers saying she did not delay the flight.
The DGCA rules allow airlines to charge additional fee for a seat of a passenger's choice, which include front row seats with extra leg room as well as aisle and window seats.
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"But due to non-availability of the seats of her choice she was booked on emergency exit seats, which also have similar leg room," said the official.
When Sen boarded the plane with her wheelchair-bound mother, she was told by the cabin crew that rules do not permit wheelchair-bound passengers to sit on emergency exit seats, said Air India.
Following this, the TMC MP "shouted and screamed" at the cabin crew, the airline claimed.
This forced the pilot to come out of the cockpit, who offered business class seats to the MP's mother but Sen declined, according to the airline.
Sen did not respond to calls or SMSes.
The airline said that it has initiated a probe into the incident.