People inside the 16-storey building waved towels at windows to signal for rescue, broadcaster RTHK said, adding that the fire had started at a gym there. Some surrounding roads had to be sealed off, disrupting morning rush hour traffic.
Around 150 people were evacuated to safety, the city's government said, while 40 people were sent to public hospitals.
Hong Kong Chief Executive John Lee said he had instructed authorities to make an "all-out" effort to treat the injured, while different government departments were investigating the cause of the fire.
The blaze, rated three in the city's five-grade system, was brought under control by 8:54 a.m. (0054 GMT), an hour after fire services were alerted to the fire in Jordan, an area teeming with homes and offices across the harbour from the financial centre.
At least six of the injured were in serious condition, the hospital authority said, with one critical.
Fire fighters were still battling on Wednesday to put out a separate massive blaze 15 hours after it erupted at a building site in the northern New Territories, a fire services spokesperson said, but no casualties were reported.
