The "well developed" fire broke out at around 2.30am according to South Wales Fire and Rescue, which said they were able to limit the damage to the shop's main store.
It said: "Crews were faced with a well-developed fire in an outbuilding that adjoined the vast main store. The incident commander dynamically appraised the situation and requested an additional four fire engines, an aerial ladder platform, three water bowsers, an incident command unit and multiple officers.
"At the height of operations there were approximately 60 firefighters involved. At approximately 5am the fire was surrounded and brought under control."
They quickly mobilised crews from the nearby Pontyclun station following reports of the fire.
