At least 17 people have also been also injured, the Erawan Medical Emergency centre told AFP.
The cause of the fire has not been confirmed.
Bangkok’s governor, Aswin Kwanmuang, told a Wednesday night news conference that an investigation into the blaze would start on Thursday.
He also said the building would remain closed until deemed safe by officials.
The shopping centre’s website describes it as the largest lifestyle shopping destination in Bangkok.
It is also said to be as the 11th largest complex of its kind in the world.