Local witnesses said they saw the black smoke rising from a fire on the fourth level of the 25-storey building at 7pm.
More than 10 fire trucks with 60 fighters rushed to the scene to stamp out the fire in two hours.
Some claimed said that the fire might be caused by electrical leakage on the fourth or fifth storey of the building.
By 10pm, hundreds of residents had to camp out.
The Phuc Thinh residence quarter has three buildings put into operation in 2004.
Some images of the fire: