© Associated PressThe flight was carrying 137 passengers
The flight, coming from Bahrain, was carrying 137 passengers and six crew. An inquiry has begun into the accident.
Officials say the runway is closed and several flights have been diverted.
Reports said some passengers jumped down from the aircraft in panic through the emergency door even before the ladder was brought to the flight.
'Jumped too soon'
"The Gulf Air flight GF270 deviated from the runway at 0355 [2225GMT] this [Monday] morning," news agency Press Trust of India (PTI) quoted airport director ACK Nair as saying.
The plane went into a muddy area, damaging its nose wheel, PTI reported.
Mr Nair said because the nose of the plane was damaged, the emergency ladder did not work.
"So a rescue team started bringing ladders to the site. But before they arrived, people began to jump," AFP news agency quoted Mr Nair as saying.
"All those injured were injured because they jumped out too soon."
One passenger has been admitted to a nearby hospital while the others have been discharged after first aid, he said.
Officials said it was very windy and raining heavily at the time of the landing.
"The preliminary investigation revealed bad weather and poor visibility caused the accident," AFP quoted an unnamed airport official as saying.
The Directorate General of Civil Aviation (DGCA) has launched an inquiry into the incident.
In May last year, a passenger plane overshot the runway while landing in the southern Indian city of Mangalore, killing 158 people.
The Boeing 737 overshot the airport's hilltop runway as it tried to land and burst into flames in the valley beyond.
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