The Times of India reported police arrested Mishra late on Friday after the airline filed a complaint on January 4.
On Saturday, a Delhi court sent Mishra to judicial remand for 14 days while rejecting a plea by officers for his custody.
Mishra’s lawyers claimed the woman “condoned” the act, according to multiple reports in India.
But his employers said the 34-year-old’s contract had been “terminated” due to the “deeply disturbing” allegations on November 26.
Air India chief executive officer Campbell Wilson revealed in a statement: “Internal investigations into whether there were lapses by other staff are ongoing on aspects including the service of alcohol on flight, incident handling, complaint registration on board, and grievance handling.”
The Tata group-owned airline also grounded the staff after facing a widespread backlash.
The carrier had earlier banned Mishra for 30 days, with social media users slamming it as not enough.
A second similar incident occurred last month on a flight from Paris to Delhi when an inebriated passenger urinated on an empty seat.
Mr Wilson added: “Air India acknowledges that it could have handled these matters better, both in the air and on the ground and is committed to taking action.”