A statement from the hospital said an oxygen cylinder exploded and there was a "small fire in a single bay".
Staff transferred 12 patients to other wards in the hospital and extra staff were called in to help care for them.
Several RUH staff were treated for the effects of smoke inhalation. The ward is expected to reopen later.
James Scott, the hospital's chief executive, said the patient who sustained injuries was burnt on the leg and was transferred to the regional burns unit at Frenchay Hospital, in Bristol.'Scorch marks'
Mr Scott said the patient had a "stable night" following the incident.
Three of the patients in intensive care were transferred to ordinary wards while five were looked after in theatre recovery.
Another three were transferred to other intensive care wards in Bristol after the explosion on Tuesday night.
"There's quite a lot of scorch marks on the wall and the unit is currently closed but we're working hard to get it reopened," Mr Scott added.
A cause for the explosion has yet to be identified and Mr Scott said an investigation would be carried out by the "relevant authorities".