The inbound plane, from Dubai, was carrying 183 passengers and six crew members when it veered off into a muddy patch of grass.
No-one was injured when the IX384 flight skidded off the runway at about 5:30 that evening.
In photos on social media the red and white plane can be seen sitting at an angle to the runway, as passengers disembarked from the front stairs and emergency crews gathered around.
Airline officials told local media "tailwind and a wet runway with inadequate braking action" were to blame for the accident.
A spokesperson for the airline said an internal investigation was underway and the director general of civil aviation had been informed.
The runway has been closed as officials investigate.
Elsewhere, in the western state of Gujarat, a Spice Jet plane skidded on a wet runway at Surat airport later that evening.
Local media reported no one was hurt in the second incident.
More about: AirIndia Express
