Groups of passengers sat dazed on the pavement near where the train derailed, some bleeding and being treated by medics. Others were taken away on stretchers by paramedics, television news footage showed.
Three people who were seriously injured have already been taken to hospital according to state-run broadcaster RTHK.
"It was driving too fast," a female passenger told Cable TV News adding that the train lost control when it was making a turn.
"It was very chaotic inside the train, there was some blood," she said.
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"It was like a ball game where everybody was bouncing around...We didn't even know what happened and then we all fell onto the floor," another passenger told the channel.
Footage showed the derailed train with its front car angled to one side with a smashed windscreen.
"There was a derailment on the light rail," a police spokeswoman told AFP, confirming that 62 people were injured. Police said the incident happened in the early afternoon at the Tong Fong Tsuen stop in the rural Tin Shui Wai district of the city.
The light rail links 68 stops along 36 kilometres (22 miles) of track in the northwestern New Territories, a semi-rural region in the north of Hong Kong.
Its single-decker cars, which can take around 200 passengers, are connected to overhead electric cables and run along tracks on the streets which also branch off into the surrounding countryside.
Accidents are rare on the southern Chinese city's public transport system, which it promotes as one of the best infrastructures in the world.
A report into the incident near Lamma Island found a "litany of errors" contributed to the crash and slammed the city's marine department for "systemic failings" in safety standards.
In November two chefs who worked at top British chef Heston Blumenthal's The Fat Duck restaurant were killed in Hong Kong when their taxi was crushed between two buses.
And in December, 24 people were injured, four seriously, after a bus collided with a coach near Hong Kong International Airport.