Seventy-four people had been rescued so far off Lamma island, an area popular with tourists and expatriates, the government spokeswoman said.
Survivors were being taken to hospital on Lamma and Hong Kong island as the night search continued.
The accident occurred over a long holiday weekend in Hong Kong, which is celebrating the mid-autumn festival as well as China's National Day on October 1.
Thousands of Hong Kong residents reside in outlying islands such as Lamma, which lies about three kilometres (two miles) off the southwest of Hong Kong island.
Hong Kong is one of the world's busiest shipping channels, although serious accidents are rare. (Reporting by Tan Ee Lyn and Donny Kwok; Editing by Anne Marie Roantree and Robert Woodward)
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