The man, in his 70s, had been attending a crayfish party at the Skansen Aquarium in Stockholm on Tuesday.
According to police, the man had his "arm on the wrong side of the security glass" when he was bitten.
The animal is one of two Cuban crocodiles at the aquarium. Both were gifted to Russian cosmonaut Vladimir Shatalov by Fidel Castro in the 1970s.
Head of the aquarium Jonas Wahlstrom told Aftonbladet that the man was giving a speech at the time of the incident.
Attendees used napkins to stop the bleeding as they waited for an ambulance to arrive.
Mr Wahlstrom said that the aquarium would be assessing the animal's enclosure to ensure it doesn't happen again.
"Nothing like this has ever happened with these crocodiles before, we've had them for more than 40 years."
Mikael Petterson, police control room officer, told local media that the man was "heavily bandaged" when officers arrived at the scene.
The two crocodiles, Castro and Hillary, were given by Fidel Castro to Russian cosmonaut Vladimir Shatalov in 1978. According to Spanish newspaper La Vanguardia, Mr Shatalov donated them to Moscow Zoo when they became too large and dangerous.
They were then gifted to the aquarium in Stockholm in 1981, as it had better facilities to care for the animals.
In 2015, Mr Wahlstrom personally took 10 of the crocodiles' offspring to Cuba as part of the island state's efforts to boost its numbers of rare species.