The blaze broke out during the night in a nine-floor building, home to about 150 residents, according to the official Vietnam News Agency (VNA).
The fire was brought under control at roughly 2am, authorities said.
Television footage showed firefighters equipped with hoses and ladders at the scene by night and thick, dark smoke billowing from the building by day.
At least 70 people were rescued but dozens of people remained trapped in the building until after dawn, state media reported. Several of the victims were admitted to local hospitals with multiple injuries after having jumped from their windows to escape the blaze.
The cause of the fire is unclear but police have detained the building’s owner, Nghiem Quang Minh, on suspicion of violating fire-prevention regulations.
A witness told the AFP news agency that they had seen a little boy thrown from a high floor to help him escape the flames.
“The smoke was everywhere. I don't know whether he survived or not although people used a mattress to catch him,” she said.
Concerns have previously been raised over fire safety in Vietnam's densely populated cities.
The building where the fire erupted was known as a “tube house” - a narrow, elongated property that is several stories high.
Prime Minister Pham Minh Chinh visited the site of the blaze on Wednesday and called for the completion of anti-fire regulations at small-sized apartment buildings and in densely populated residential areas, according to a government statement.
He said: “We must take this as a lesson” to improve fire prevention and firefighting, he said, adding that “regulations must be taken seriously so we can avoid a tragedy like this.”
Mr Chinh added: “Such a high-rise building, up to 10 floors, which looks like a mini apartment block, has no escape route. It is unacceptable when [the apartment block which houses] 45 households has no exit.”
Last year, a fire at a karaoke parlor in southern Vietnam’s Binh Duong province killed 32 people.