The Airbus A340 plane from Istanbul "veered off a rapid exit taxiway" after landing at Chhatrapati Shivaji International Airport shortly before 4:15 am (2245 GMT Thursday), an airport spokeswoman said.
"Passengers are disembarked safely and taken in the terminal. No casualties reported. Flight operations have not been affected," Anindita Sinha added in a text message statement.
The airport said the runway had been inspected about 15 minutes before the incident and no problems were reported. One landing and take-off took place immediately after the inspection and before the arrival of the Turkish jet.
Turkish Airlines said in a statement that there were 104 people on board the plane, including 11 crew members.
"The passengers and the crew were immediately evacuated and no injuries reported," it added, blaming the incident on "excessive rainfall".
The "necessary analysis and research" was being carried out to determine the exact cause of the incident and a new aircraft has been sent for passengers flying from the Indian city to Istanbul, the airline added.
Sinha said that two flights scheduled to land in Mumbai were diverted and the runway in question closed for a time, leading to slight delays of other arrivals and departures which were forced to use the second runway.
On Wednesday, an Air India Airbus A330 plane from the Saudi city of Jeddah with 286 passengers and crew was forced to land under emergency conditions in Mumbai after problems were detected with its hydraulics, the airline said.
On Tuesday, another Air India jet with 123 passengers and crew landed under emergency conditions in Thiruvananthapuram in the southern state of Kerala because of a hydraulic problem.
On Monday, seven passengers were injured when they jumped out of a Gulf Air Airbus 320 from Bahrain before the emergency shoots deployed after the jet skidded to a halt on landing in Kochi, also in Kerala state.
Copyright AFP (Agence France-Presse), 2011