The fire started just before midnight on Tuesday (1700 GMT) in the parking floor of the 10-storey building, an area packed with motorbikes, witnesses said.
More than 100 people managed to escape or were pulled from the building by rescuers, with authorities rushing 54 to hospital, including "dozens of dead", the official Vietnam News Agency said.
The deputy minister of public security, Le Van Tuyen, said that "the number of losses in the fire was huge", state media reported, although authorities have yet to release an official toll.
At least three children were among the dead, according to reports.
"I heard a lot of shouts for help. We could not help them much," said Hoa, a woman who lives near the block and gave only one name.
"The apartment is so closed with no escape route, impossible for the victims to get out," she told AFP at the site.
Photos by AFP photographers on the scene overnight showed flames and smoke billowing from barred balconies.
The blaze was out by Wednesday morning, but rescuers still struggled for hours thereafter to access the building, which is down a narrow alley in a residential area of southwest Hanoi.
The complex's small balconies were surrounded by iron bars, with the apartment block having only a single exit -- and no emergency ladder on the outside.
Around 150 people lived in the complex, authorities said.
Another witness, Huong, said a small child was thrown from an apartment to escape the flames.
"The smoke was everywhere. There was a little boy thrown from a high floor, I don't know whether he survived or not although people used a mattress to catch him," she said.
'We were so scared'
Neighbours reported several others jumping from the block.
"There was a middle-aged woman jumping down onto my terrace here. She hit her arm and broke it. Another person also jumped down here and broke their legs," said Dao To Nga.
"A child was put into a plastic basket and lowered down".
Some were able to flee the building using her roof. "This rooftop of my family helped 14-15 people escape," she said.
One survivor, Nguyen Thi Minh Hong, told AFP that her family waited in their seventh-floor apartment at the back of the building for five hours before help arrived.
"We were sleeping when suddenly we felt very hot because the power had been cut. My husband opened the door and we heard people shouting for help and we saw smoke," the 34-year-old said.
The family, which included her two children aged six and nine, tried to escape to the roof but were forced back into their apartment due to the heat of the fire.
"I was so scared. We stayed inside the room for five hours... I just tried to calm my kids down by holding a wet towel to their face," she said from Hanoi's Bach Mai Hospital.
"We were between life and death."
Later, hundreds of people gathered outside a Hanoi morgue, waiting to hear if their family members and friends were among the victims.
One group of five women, sitting on the floor outside the morgue, said their "whole family had gone".
"They were our children and grandchildren," they said.
Survivors in shock
Prime Minister Pham Minh Chinh, who visited the site Wednesday, ordered an investigation into the fire.
At a visit to survivors at Bach Mai Hospital, Chinh was told by clinic director Dao Xuan Co that two of his patients were in serious condition, while 22 were recovering from minor injuries.
"However many of them were in shock," he told Chinh, adding they were receiving psychological treatment.
Vietnam has experienced several deadly fires in recent years, frequently at entertainment venues.
A year ago, a karaoke bar blaze in commercial hub Ho Chi Minh City killed 32 people and injured 17. The owner was later arrested on charges related to breaching fire prevention regulations.
In the aftermath, the prime minister ordered an inspection of all high-risk venues.
Thirteen people died in 2018 after an apartment complex, also in Ho Chin Minh City, caught fire.