Firefighters battled the blaze into the night, with thick black smoke billowing from the 31-storey towers and orange flames lighting up the night sky.
The Wang Fuk Court housing complex, where the fire started, is home to 2000 residential apartments, comprising eight blocks.
The Fire Services Department told Reuters it does not yet have a figure for the number of people who may still be inside the buildings.
One resident surnamed Wong, 71, broke down in tears and sobbed, saying his wife was trapped inside one of the buildings.
A firefighter surnamed Ho was among the 14 killed, the director of Fire Services said and more than ten people have been injured.
Harry Cheung, 66, who has lived at Block Two in one of the complexes for more than 40 years, said he heard "a very loud noise at around 2.45pm" and saw a fire erupt in a nearby block.
"I immediately went back to pack up my things," he said.
"I don't even know how I feel right now. I'm just thinking about where I'm going to sleep tonight because I probably won't be able to go back home."
People gathered on a nearby overhead walkway, watching in dismay and taking pictures as smoke billowed from the buildings, some of which were clad in bamboo scaffolding, with social media posts from residents saying the units had been under renovation for about a year.
Frames of scaffolding were seen tumbling to the ground as firefighters battled the blaze while scores of fire engines and ambulances lined the road below the development, according to Reuters witnesses.
Wang Fuk Court is one of many high-rise housing complexes in Hong Kong, which is one of the most densely populated areas in the world.
Tai Po, located near the border with mainland China, is an established suburban district with a population of about 300,000.
Owning a home is a distant dream for many in Hong Kong, one of the world's most expensive housing markets and where residential rents are hovering near record highs.
The complex is under the government's subsidised home ownership scheme.
It has been occupied since 1983, according to property agency websites.
The fire department said it received reports at 2.51pm that a fire had broken out in Wang Fuk Court.
By 6.22pm it had been upgraded to a No 5 alarm, the city's highest.
Strong winds fanned the flames causing the blaze to spread to seven of the complex's eight blocks.
Hong Kong is one of the last places in the world where bamboo is still widely used for scaffolding in construction.
The government moved to start phasing out the city's use of its bamboo scaffolding in March, citing safety.
It announced that 50 per cent of public construction works would be required to use metal frames instead.
