The man, named locally as Max Berryman, was part of a crew that caught the porbeagle shark at about 8.15am on Sunday.
The 21-year-old was trying to put the animal back in the sea when it attacked him, the Maritime and Coastguard Agency said.
Dramatic footage captured by the agency shows Mr Berryman, from Penzance, being hoisted up into an air ambulance in heavy winds.
The fisherman can be seen clutching on to paramedic and winchman Julian Williams, who had jumped from the side of the boat whilst wearing a harness.
A second air ambulance crew member can be seen inside the helicopter holding on to the cable attached to Mr Williams as the pair sway above the sea.
Mr Berryman was then taken to a hospital in Truro, according to reports.
The crew on the 23m Govenek of Ladram vessel had sterilised and dressed his leg wound before alerting the coastguard by radio.
The coastguard search and rescue base in Newquay sent the helicopter to the boat, which was positioned 107 nautical miles (123 miles) west from Lands End.
Mr Williams said: “The crew had done a really good job of dressing the wounds before we arrived, which meant that we were able to save time getting the casualty to Treliske hospital.
“We understand that the porbeagle shark was on the deck when the incident happened, but as the crew were attempting to put it back in the sea one of the fisherman was bitten in the process.”
Alex Grieg, senior maritime operations officer for HM Coastguard, said: “Thanks to the efforts of the crew on board and their swift actions in treating the wounds and contacting us, we were able to arrange the evacuation of the crew member promptly and get him to hospital.
“We understand the fisherman is still in hospital and wish him a speedy recovery.”
Porbeagles are a type of a mackerel shark found off the coast of the British isles in warm summer months.
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They generally stay out to sea where they hunt mackerel, herring and squid.
The sharks typically reach 8.2ft (2.5m) in length.