According to The Telegraph, Fry suffered minor scratches and bite wounds.
He was driven to a nearby hospital by his companions instead.
The 25-year-old man had been surfing with three others at Avoca Beach, 95 kilometres north of Sydney.
Mr Fry said he had "no idea" what kind of shark it was, but said it was "big and scary".
"It was terrifying but it only lasted five seconds".
Avoca Beach and North Avoca have been closed for 24 hours following the ordeal.
The doctor watched a YouTube video featuring an interview with the Australian surfer, who punched a shark to survive an attack during a competition in South Africa in 2015. A great white shark and a bronze whaler shark were both been "spotted" by lifeguards.
N. Korean soldier, shot and wounded, defects to South
The attack prompted Washington to fly nuclear-capable B-52 bombers toward the DMZ in an attempt to intimidate North Korea. North Korea and South Korea have been in a technical war since the conflict of 1950-53 ended with an armistice.
DC Fires Eddie Berganza
DC Comics and Warner Bros. have parted ways with longtime editor Eddie Berganza after he was suspended over the weekend. The third woman, who wants to remain anonymous, said Berganza forcibly kissed her at a comics convention in March 2012.