The beachgoer, Mark Hickey, swam 15-20 metres (50-65 feet) from the shore of Clarkes Beach to retrieve the man, who had sustained severe wounds to his right leg, Police Inspector Bobbie Cullen said.
The victim, a local man in his 50s whose name has not been released, received medical treatment on the beach but did not survive, Cullen said.
"A gentleman who was on the beach went out and located the gentleman and pulled him in," Cullen told reporters. "Absolutely it is (an extraordinary act of bravery) and we can only thank him for his efforts."
"I went out there and, I don't know, I just thought I've got to get this guy in and that's what I tried to do," Hickey said.
He said he dragged the victim onto the beach and attempted to resuscitate him for 20 minutes, but the man had apparently bled to death in the water.
Ten reported that the shark had bitten through the victim's wetsuit on his upper right thigh, tearing off much of his leg.
Cullen said the crew of a rescue helicopter spotted what appeared to be a great white shark in the area after the suspected attack, but had lost sight of it. She said all Byron Bay beaches would be closed for 24 hours due to the potential danger.
Byron Bay is a renowned surfing location near Cape Byron, the most easterly point of the Australian mainland, about 800 kilometers (500 miles) north of Sydney.
The death is the first fatal attack in Australia since April 3, when a 63-year-old woman was taken by a 3-to-4-meter (10-to-13-foot) shark near the village of Tathra, 340 kilometers (210 miles) south of Sydney.
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