Ryan Boarman, in his 20s, was admitted to hospital in the west of the holiday island Monday shortly after being attacked by the shark as he surfed at Balian beach.
While shark attacks are generally rare in Bali there have been several such incidents in recent years at Balian, a popular surfing spot.
Doctor Ni Gusti Ayu Made Sri Pujarini, who initially treated Boarman at a local hospital, said he was conscious when brought in.
Pujarini said he underwent emergency surgery and was then transferred to a bigger hospital in the Balinese capital Denpasar.
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Twiggy Van Ryan, an Australian who lives near Balian, described how he saw Boarman shortly after the attack and helped dress his wound before he was taken to hospital.
"It was a pretty heavy wound, maybe four inches (10 centimetres) either side of the tip of the elbow, basically his whole elbow had gone into the shark's mouth and then was pretty badly damaged as the shark pulled back," he said.