Footage has emerged of USA navy sailors embarking on a rescue mission in the aftermath of the plane crash - using an inflatable boat to shuttle people ashore before the plane sank in about 100ft (30m) of water.
In a statement, Air Niugini thanked the locals who had rushed to the plane's aid.
Within minutes, local fishermen were on the scene with a flotilla of small motor boats to rescue people.
The Federated States of Micronesia is a nation made up of over 600 islands in the Pacific. Both the airline and the US Navy said the plane landed in the lagoon short of the runway. The airline said the plane landed short of the runway.
His age and nationality is unknown, but Air Niugini says it is working with local authorities, hospitals and investigators to try and find him.
Passenger Bill Jaynes said the Air Niugini plane came in very low.
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Airplane crashes into ocean after it overshoots runway in Chuuk
The PNG Accident Investigation Commission was sending a team to the accident site, the ABC reported. People in small boats were seen rescuing people from the plane before it began to sink.
After the crash, all flights in and out of the Chuuk International Airport were suspended.
Papua New Guinea's Accident Investigation Commission (AIC) said it was preparing to send investigators to Weno. While the flight services to the island are limited, United Airlines operates a well-known "Island Hopper" flight across the Pacific from Honolulu to Guam that stops in five locations, including Chuuk.
Air Niugini scheduled a special flight "to allow those passengers who wish to complete their trip to Port Moresby and onward to their final destinations".
The AIC website details an incident involving the aircraft in May this year when a Hercules operated by a freight company clipped the 737's wing while taxiing, causing "significant damage".
Micronesia, located north of Australia and east of the Philippines, is home to just over 100,000 people.
"We were able to get out, the water was only up to about here on me, inside the plane, and we went out the emergency exit doors", Jaynes said. It has close ties with the USA under an agreement known as a compact of free association.