The victim was airlifted to hospital in the early hours of Monday morning, according to Sgt Colin Taylor.
He wrote on the Isles of Scilly Police Facebook page: "The swift action of the Medical responders on the island was first rate.
"I attended with the paramedic based on St Mary's on the medical ambulance boat Star of Life."
Sgt Taylor said that St Mary's Police are investigating the incident and are not asking for further witnesses.
He added: "A knife has been recovered. A suspect has been identified who is no longer on the islands."
Sgt Taylor said that he worked a 19-hour shift and warned: "Knives are very dangerous when used as weapons. This is why there are sound laws to enable us to seize fixed blade, locking knives or knives over a specific length that a person does not have good reason to possess in public."
These sort of incidents are extremely rare on the Isles of Scilly, a place Sgt Taylor once described as 'The Land that Crime Forgot'.
However, as one poster to his Facebook page pointed out: 'Fill someone with drinks or drugs, give them a knife and somebody to argue with and it won't matter where they are - the Isles of Scilly or the middle of New York'.