The blaze began at around 1am local time in the basement parking area of the six-year-old Carina Plaza in Ho Chi Minh City.
The complex is made up of at least three buildings, with 736 apartments, and the flames quickly spread.
Each of the buildings has between 14 and 20 storeys.
Hundreds of people were trapped inside as 200 firefighters with more than 30 fire engines worked to extinguish the flames.
Local media footage showed firefighters on high-rise ladders helping people to escape from their balconies. Many residents shined torches to call for help.
An unidentified fire official said: “Most of the victims died from smoke inhalation, but we also found people who had died jumping from high windows.”
He added that the 27 people injured were in a stable condition and firefighters were still searching the block to make sure no one was still trapped.
Around 100 people were rescued and 1000 escaped by themselves, state media said.
News website VnExpress quoted resident Le Thi Cam as saying: “We were sleeping when the fire alarm went off, we all rushed out to the staircases.
“It was very hot and dark.”
An unidentified male resident added: “We were awakened by loud noise.
“We ran out of the apartment but there was a lot of smoke.