Around 30 pets had to be evacuated from the Pets at Home shop while firefighters tackled the blaze in Perth, which also affected B&M and a vacant outlet.
Emergency services were called to the scene at St Catherine's Retail Park around 2am on Saturday. Police are treating the blaze as suspicious.
Chief Inspector Ian Scott, Perth And Kinross local area commander, said: "Our inquiries have given us reason to believe that there may be a person within the building.
"Our investigation into the fire is being conducted with this possibility in mind and efforts are continuing to make the building safe to enter, at which point it will then be fully examined.
"We believe that we know the identity of the individual and specialist officers are providing support to their family at this time.
"The damage to the building is extensive and we are working closely with the Scottish Fire and Rescue Service and other partners to establish the full circumstances.
"We will maintain a police presence at the scene until the investigation is complete. This may take some time and I would like to thank the local and business community for their support."
It is currently too dangerous to enter the property and work is under way to make it safe.
There were no reports of any injuries.
Police said there will be no pedestrian access between Glasgow Road and Morrisons until the area has been made completely safe.