Authorities said 41 people were injured and some 300 more were evacuated after the blaze began at the 13-storey building in the city's Yau Ma Tei neighbourhood shortly after 7:53 am (2353 GMT Tuesday).
Hundreds of firefighters put out the fire at the 60-year-old building after several hours rescuing 250 people with 50 more evacuating themselves, Lam Kin-kwan, a local fire department official, told reporters.
Among the injured were 38 hospitalised with burns and inhalation injuries, said assistant chief ambulance officer Tong Sze-ho.
Local broadcasters showed images of some residents waving towels from their windows to appeal for help while others rushed to the building's rooftop.
Lam said the fire started outside a fitness centre on the first floor and quickly began to spread to the upper floor.
Hong Kong leader John Lee said in a statement he was "deeply saddened" by the deaths and injuries and extended his condolences to the affected families.
Hong Kong has some of the world's most densely populated -- and tallest -- apartment blocks.
Deadly fires used to be a regular scourge, especially in poorer neighbourhoods.
But in recent decades safety measures have been ramped up and such fires have become much less commonplace.
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