The aircraft was en route from Honolulu to the island of Maui, but went down in the water soon after take-off from Daniel K Inouye International Airport. The US Coast Guard rescued the pilots.
One was found clinging to the plane's tail and airlifted to safety. According to officials from the state's transport department, quoted by local outlet Hawaii News Now (HNN), he was airlifted to Queen's Medical Centre and taken to intensive care in critical condition.
Rescuers brought the other pilot to shore by boat, HNN said. He is reportedly in a serious condition with a head injury.
Footage broadcast by NBC shows a man thought to be one of the pilots being taken away in a wheelchair. He appears to be conscious.
The pilots knew they were in trouble. 'We've lost number one engine,' a crew member tells air traffic control, according to a recording posted online.
'We're going to lose the other engine, too. It's running very hot.'
This aircraft is not the same as a Boeing 737 Max, the aircraft temporarily grounded by authorities after two fatal passenger airline crashes in 2018 and 2019 respectively.
The 737 Max was cleared to fly again by US regulators in 2020, but it recently came under further scrutiny.