The 72-year-old man received fatal wounds in the attack on Saturday at Second Beach in Port St. Johns, where he and his wife were part of a tour group, the institute said in a statement. It did not name the victim.
It added the species of shark involved in the incident was not immediately known.
South Africa’s coast is known for its great white sharks, which are an attraction for its tourist industry with operators offering cage dives and boat trips to view one of the ocean’s fiercest and most feared predators.
Underwater fences have been erected at popular swimming spots for protection.
In October, a man who was snorkeling was fatally attacked by a shark off the Eastern Cape coast.
According to the University of Florida’s latest annual International Shark Attack File released in February, shark attacks around the world fell to a five-year low in 2013, but the number of fatalities rose with the most incidents recorded in Florida.