The 25-year-old, named in local media as Charlie Fry, was surfing with three others at Avoca Beach in New South Wales state north of Sydney on Monday when the shark "jumped out of the water and hit him in the right shoulder", police said.
"I saw a shark's head come out of the water, with its teeth, and I just punched it in the face," Fry told commercial broadcaster Channel Nine Tuesday.
"It was just pure adrenaline, I genuinely thought I was going to die, like 'you're about to be eaten alive by a shark', so everything slowed down, like 'get on your board and surf'."
The Briton thought the shark was up to six feet long (1.5-1.8 metres), although a local helicopter rescue service said later that a three metre great white and a three metre bronze whaler shark were spotted off Avoca.
Fry, who was able to surf back to the beach with his friends, was not seriously hurt and initially did not even realise he had been bitten.
"It could have easily taken my hand. I count myself very lucky."
There have been 16 shark encounters and attacks off the island continent's vast coastline this year, including the death of a 17-year-old girl mauled in full view of her parents in Western Australia.
Experts say incidents are increasing as water sports become more popular and baitfish move closer to shore, but fatalities remain rare.
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