"The pilot threatened that he would not fly without his mother."
The pilot said that his mother was sick and he could not leave her at the airport, the paper reported.
"The GM (general manager)... investigated the matter after it was brought to my notice," Air India chairman Rohit Nandan told the Express, adding that disciplinary action was being taken.
Air India pilots are allowed some free tickets for themselves and family members subject to seat availability.
The duty manager's report recorded that the fully-booked flight, with 122 passengers on board, was delayed for 20 minutes because of the incident.
An Air India spokeswoman told AFP on Sunday that the airline was not immediately available for comment.