The Boeing 737, en route from Dubai, skidded off the runway in rain and broke in two after landing at Calicut airport, aviation officials said.
The flight was repatriating Indians stranded by the coronavirus crisis.
Prime Minister Narendra Modi said he was "pained by the plane accident".
The rescue operation at the crash site has now been completed and survivors have been taken to hospitals in Calicut and Malappuram, according to Kerala Chief Minister Pinarayi Vijayan.
Dozens of people were injured, 15 of them seriously, a senior police officer said.
Air India Express said the two pilots were among the dead.