The fire happened above Candy Love, in Montague Street, at around 12pm.
The man has been taken to hospital because of smoke inhalation.
Candy Love owner Paul O’Brien called the fire brigade when a member of staff phoned to tell him the shop’s alarms were going off.
He said: “There was thick black smoke and from what I could see, it was pretty bad.
“I called the fire brigade and managed to get another couple out of the building.
“They just pulled someone out but I don’t know how bad it is yet.”