The 39-floor World Trade Centre is home to restaurants, offices and shops in the bustling Causeway Bay commercial and shopping district.
The fire broke out in a utility room on a lower level of the building's mall at noon, media said, before it spread to bamboo scaffolding cladding the exterior.
City authorities said firefighters had battled the blaze with two high-powered hoses, using ladders and breathing apparatus in their effort to rescue those trapped.
Police told Reuters 13 people were taken to hospital, one of them semi-conscious.
"The fire was extinguished at 1630 hours (0830 GMT)," the fire department told Reuters.
Earlier, shoppers and office workers streamed out of the building as smoke billowed from it and police blocked off traffic on major adjacent roads.
About 100 people moved from a restaurant to the top 39th floor when the fire broke out and smoke filled the dining area, broadcaster RTHK quoted police as saying.
The cause of the fire was not immediately clear.
By Edmond Ng.
(Reporting by Sonia Cheema, Edmond Ng and Anne Marie Roantree; Editing by Clarence Fernandez and Andrew Heavens)
epa09642657 The World Trade Centre building (R) in Causeway Bay, Hong Kong, China, 15 December 2021. Around 1,200 people were evacuated from the building following an electrical fire that injured at least 13, while hundreds were still trapped on the roof. EPA-EFE/JEROME FAVRE