According to the South China Morning Post, the fire broke out after 11:30 a.m. (3:30 GMT). The newspaper has updated information, noting that there were at least 25 people on board.
"An initial investigation showed there was an explosion and some people fell into the waters from the vessel", a police spokesman said, as quoted by the newspaper.
The rescue operation is underway, with fireboats and a government helicopter dispatched to the area.
Hong Kong police have shared the information about the incident on their official Facebook account.
Meanwhile, the broadcaster RTHK reported that one person had been killed, while 23 crewmen had been rescued, with three to four of them in need of medical treatment. Three other crewmen are still missing. The vessel in question is reportedly the Vietnam-flagged oil and chemical tanker Aulac Fortune.