Ethan McKen, 24, was at the Black Sea resort of Sunny Beach, near Burgas, when he and a friend were hit by a wave, earlier on Saturday.
Mr McKen was unable to get back to shore and his friends were unable to reach him, a family member said.
Travel agent Thomas Cook is working with local authorities to find him. The UK Foreign Office has been made aware of the incident.
Its spokesman said it was providing consular assistance to the family of a British man.
A spokesman from Club 18-30, which is owned by Thomas Cook, confirmed one of its customers staying at its Sunny Beach resort went missing earlier on Saturday.
A second person is safe and recovering in a local medical centre.
He said: "We are liaising closely with the British Embassy and the local authorities as the search effort continues, and can confirm that the local police are stopping anyone entering the water at present while this continues.
"Club 18-30's parent company Thomas Cook is liaising closely with the missing person's family in the UK, and are arranging for relatives to travel to Bulgaria at the first available opportunity."
A teacher from Nottingham has been swept out to sea in Bulgaria.