The victims have been transferred to local hospitals, although their conditions are not known, Hong Kong officials said.
A 60-year-old man has been arrested and accused of arson, Hong Kong police said at press conference Friday.
The man, whose last name is Cheung, was critically injured and told police he set the fire, authorities said.
Police said they believe the fire was an isolated incident carried out for personal reasons. There is no evidence it was terror-related, they said.
The fire happened at the Tsim Sha Tsui station on the Tsuen Wan Line. The station, one of the busiest on Hong Kong's Mass Transit Railway, has been closed for the time being.
Local media reported that a person threw a flammable liquid inside a crowded train compartment.
Video and pictures circulating on social media show a man with his trousers on fire, lying on the floor of the station platform as other passengers frantically put out the flames.
In a statement, Leung Chun-ying, Hong Kong's chief executive, said he's paying close attention to the incident and has asked all departments involved to put their full efforts into the investigation.
Leung expressed his deepest condolences to the injured and wished them a quick recovery.
He also asked Hong Kong's secretary for food and health to visit the injured in the hospital.