The Boeing 787 Dreamliner hit a residential area near the airport shortly after leaving the track, apparently touching an inn for medical staff.
The plane carried 232 passengers and 12 crew members.
The authorities have said that some ground residents are probably dead, although the exact figures remain vague.
Images of the scene show thick smoke and parts of the plane embedded in a building. Emergency services transported the injured to neighboring hospitals, and Air India has set up an assistance line for affected families.