Fire crews were called to ward 12 of Singleton Hospital on Sunday night.
No-one was injured, but some of the 36 patients who may have inhaled smoke are being monitored as a precaution.
Abertawe Bro Morgannwg University Health Board said it is working hard to keep disruption to a minimum, but advised there may be some knock-on effects.
Chris White, the health board’s chief operation officer, said some planned procedures were being postponed as a result of the fire.
He added: “There may be some knock-on effects to our services as a result of temporarily losing these beds.
“Morriston and the Princess of Wales hospitals are extremely busy, and because of the situation at Singleton there is less flexibility for intra-hospital support.
“The damage to ward 12 will be assessed later, but it is likely that the ward will be out of use for some time.”
The health board is asking people who do not have a serious illness or injury to seek alternative methods of treatment.