The blaze broke out on Wednesday in the afternoon and spread quickly along the bamboo scaffolding that surrounded the building.
Thick smoke rose above the area as firefighters worked from ladder trucks to contain the flames.
Hong Kong's chief executive, John Lee, confirmed at least 36 people, including a firefighter, had died and another 279 people were reported missing.
Hundreds of residents were evacuated as the blaze spread across seven of the eight buildings in a housing complex in Tai Po district, a suburb in the New Territories.
At least 29 others remained hospitalized.
