David Lilienfeld, 20, was surfing with his brother, Gustav, 18, and several friends Thursday when he was attacked, the Independent On Line reported.
National Sea Rescue Institute spokesman Craig Lambinon said the victim "sustained complete amputation of his right leg, below the hip," The Sydney Morning Herald reported.
The shark was believed to be at least 15 feet long, authorities said.
Lucille Bester who was picnicking on top of nearby cliffs with her husband said they spotted the shark and tried to warn the surfers they saw in the water.
"We started screaming from the top that there was a shark ... we didn't know how to get down the mountain but they could not hear us," she said. "The shark disappeared but the next thing we saw the shark come from under one of the guys and grab him. The shark shook him and then let him go. The surfer was screaming -- it was terrible."
She said the man disappeared again and that time she could see blood in the water.
Notable deaths of 2014 [PHOTOS]