Video posted on social media showed a wall of dark gray smoke and orange flames billowing out of one end of the five-story building in the city of Taichung, AP reported.
The cause of the fire was undetermined but the Taichung government said it spread rapidly because of a large quantity of foam panels on site.
One person died after jumping from the third floor and the other victims were found by firefighters in a search that extended into the evening, Taiwanese media said. Nineteen people were rescued.
The building was being constructed for the PX Mart supermarket chain.
MA/PR