Calicut Airport, also known as Kozikhode International Airport, is located in the south Indian state of Kerala.
"As per the initial reports rescue operations are on and passengers are being taken to hospital for medical care," the civil aviation ministry said in the statement. There was no fire on board, it said.
Rajiv Jain, a spokesman for the Civil Aviation Ministry, said no fire was reported on the Boeing 737 aircraft after it landed.
The NDTV news channel said 30-40 people were hospitalised and other passengers have been evacuated from the aircraft.
Mr Jain said there were 174 adult passengers, 10 infants, two pilots and five cabin crew on board the aircraft.
The flight was a repatriation flight operated by the government to bring citizens home due to the coronaviurs outbreak.
Amit Shah, the Indian home minister, said in a tweet that he was "distressed to learn about the tragic accident of Air India Express aircraft at Kozhikode."
The Directorate General of Civil Aviation (DCGA) said the plane fell in to a valley and broke in to two after skidding off the end of the runway.
Narendra Modi, the Indian Prime Minister, tweeted: "Pained by the plane accident in Kozhikode. My thoughts are with those who lost their loved ones. May the injured recover at the earliest."
The death toll from an Indian passenger aircraft accident has risen to 18, while 16 people have been severely injured, a senior government official said on Saturday.
The Air India Express plane overshot the runway of the Calicut International Airport in heavy rain near the southern city of Kozhikode on Friday.
The flight was carrying 190 passengers and crew.
Local TV channels say the fuselage of the Boeing-737 broke in to two pieces on impact.
At least 18 people have died, including the pilot and co-pilot, according to local police, with at least 16 critically injured. At least four are still stuck in the wreckage.
This was India's worst passenger aircraft accident since 2010.
"We have at least 89 people, many of them with serious injuries, admitted at different Kozhikode hospitals. The ambulances are still coming in," said Sujith Das, a senior police official.
"We have been told that all those who have survived the crash also have some form of injuries."