Firefighters were called to the Toys R Us store in Kingsway West Retail Park at 00:34.
Seven appliances including an aerial unit tackled the fire in an external canopy at the rear of the building.
The Scottish Fire and Rescue Service said the store was heavily smoke-logged as a result, but the fire was extinguished within two hours.
A Police Scotland spokeswoman said officers were keen to trace a person seen in the area at the time who was wearing a light-coloured hooded top and dark-coloured trousers or jogging bottoms.
Police in Dundee are investigating whether a major fire at a Dundee toy shop was started deliberately.