The incident occurred about 50 meters off the coast in Telyakovsky Bay in southern Primorye.
The 25-year-old man was immediately taken to a hospital in the village of Slavyanka and operated on.
He is currently unconscious; doctors say he will recover, but will probably have no use of his arms below the elbow.
The species of shark is as yet unknown, but is thought to most likely have been a hammerhead.
Primorye has not seen any shark attacks for years, so it could be a signal of climate change, the head of WWF’s sea program, Konstantin Zgurovsky, told Interfax.
Zgurovsky added that sharks tend to flock to places where tourists feed the fish, which attracts more dangerous predators.
Russia’s Primorye region is not the only place to be hit by sharks this summer. According to media reports, four beaches in the Seychelles Islands were closed due to shark warnings.
Meanwhile, nature specialists say that, despite widespread belief, sharks are not the biggest threat to tourists.
“The sea has many different predators and dangerous animals,” Zgurovsky said. “There are a lot of comb jellies and jellyfish that are poisonous. In the tropics, there are worms that can penetrate the human body and then slowly kill it from the inside. Still, it is shark attacks that grab the most media attention, especially after everyone watched ‘Jaws.’ At the same time, there are many more cases when tourists die in boat collisions or drunken swimming.”