Northern Territory Police said the 23-year-old was bitten while pulling up a net about 12:00pm on Thursday, about 70 nautical miles south of Groote Eylandt.
Craig Garraway, St John Ambulance operations manager, said that authorities responded to a call from the boat for help.
It is noted that death from the bite of sea snakes - a rare phenomenon, in spite of their deadly poison.
It is not yet known which species of sea snake was involved.
Northern Territory Police confirmed the British Embassy had been notified and said a post-mortem would be conducted on the man's body.
Earlier this year, Darwin fisherman Peter Davis almost had his finger amputated after being bitten by a sea snake that was snagged on his line.
The Foreign Office confirmed it is supporting the family of a British man who died in the Northern Territory.
The 23-year-old man's death marks the second in which a British man has recently died on an Australian fishing boat.
Found in tropical and sub-tropical waters through south-east Asia, the western Pacific and northern Australia, they grow to between 120cm and 150cm but can get as long as three metres, and are considered to be non-aggressive.
While sea snakes were rarely aggressive underwater, if caught by a fisherman Dr Guinea said cutting the fishing line could be the safest option.
NT Work Safe is investigating the incident and said the prawn trawler, Ocean Exporter, is owned by WA Seafood Exporters.
NT Coroner Greg Cavanagh found his death was needless and preventable.
'It would have been prevented if there was even a modicum of compliance with the law.