The same private bus company, KMB, was involved in Hong Kong's worst traffic crash, when 21 died and 20 were injured in 2003 after a double-decker bus crashed through a guardrail and down a hill after colliding with a truck.
Firefighters are still at the spot to rescue passengers trapped inside.
Passengers quoted in local media say the bus was travelling very fast before it tipped over.
The driver has been arrested on two counts of causing death and grievous bodily harm by unsafe driving. The company said it would also set up an investigation team to probe the cause of the crash.
Early reports said the number of dead stood at 19 but that was later revised down.More news: Doctor Dolittle Reboot Casts Spider-Man, Harry Potter Stars
Dozens were injured in the wreck, police spokeswoman said. Passengers suggested the bus was speeding downhill at the time, and the driver appeared to be upset after he was told off for being late.
Lawmaker Lam Cheuk-ting of the Democratic Party urged the government to investigate bus designs, "especially with the upper deck of buses having been repeatedly torn off in accidents, posing a serious threat to passengers on the upper level".
The driver had been with the company since 2014 and was familiar with the route on which the accident happened. More than three-quarters of bus drivers work 50 to 60 hours a week, according to a 2016 survey conducted by the Hong Kong Confederation of Trade Unions.
While Hong Kong has a well-developed and generally safe public transportation system, fatal bus crashes have persisted.