The blaze at Bucharest's Collectiv club on 30 October - sparked by fireworks, which ignited foam on the walls - left at least 45 dead.
Twelve victims have since been flown by Nato to hospitals in the UK and Norway.
One patient is in a stable condition at the Welsh Centre for Burns and Plastic Surgery, Abertawe Bro Morgannwg Health Board said.
Some of those injured in the blaze arrived at RAF Brize Norton, in Oxfordshire, late on Sunday and were transferred to hospitals around the UK.
The man was taken to Swansea in a Welsh Ambulance Service emergency vehicle.
The fire led to mass protests and the resignation of Prime Minister Victor Ponta's government.
Three owners of the Romanian club have been arrested amid allegations the venue was overcrowded, lacked the required number of emergency exits, and may not have been authorised to hold such a concert.
A victim of a nightclub fire in Romania is being treated at Swansea's Morriston Hospital, a health board says.