According to the Phuket News, the blaze began around 9.40pm, when hundreds of shoppers and an estimated 1,000 staff were inside.
More than 50 fire trucks rushed to the site of the blaze, and at least 300 firefighters were involved.
As of 2am (1900 GMT), authorities remained tight-lipped about possible victims.
Phuket Vice Governor Sommai Prijasilpa and district mayors were all at the scene.
Police cleared crowds around the fire, saying they feared explosions from gas tanks inside the store, and from a nearby Esso petrol station.
The newspaper's reporter Naraporn Tuarob said early Thursday, "At the moment I can hear explosions but I don’t know where they are coming from. The flames have moved to the Thanksina wood factory."
An Iranian resident of Phuket, Rasha Shidmaher, happened to be driving by. "There were people screaming and trying to leave the area. I saw a lot of ambulances as well from all around the island," he said.
An early report said that the fire began when an electrical short circuit had ignited gas tanks, but that could not be confirmed Thursday.
The huge store is a Phuket institution, selling everying imaginable. Sections of the store operate as a "box store" where buyers purchase items in bulk.