Early reports from local media including the South China Morning Post indicate 17 men have died and two women.
Passengers quoted in local media say the bus was travelling very fast before it tipped over.
Witnesses told horrific stories of watching dazed and bloody passengers drag themselves from the mangled wreckage.
Firefighters sort through crash debris after a bus crash in Hong Kong on February 10, 2018.
Photographs of the incident showed the bus on its side with the roof torn off.
The bus was carrying a lot of passengers when it overturned on a highway in the suburbs.
Passengers said the driver was breaking the speed limit to make up for being behind schedule, according to Now News.
The bus was on its way from Sha Tin racecourse to Tai Po Centre when it flipped onto its side while attempting to turn. It was really chaotic in the bus. The driver has been arrested on two counts of causing death and grievous bodily harm by unsafe driving.
He said the franchise bus company would pay $10,000 to each injured person and family of the deceased. "People fell on one another and got tossed from side to side".
KMB general manager Godwin So Wai-kei said the 30-year-old unidentified driver joined the company in 2014 and had driven the route before.
Hong Kong's public transport is usually safe, and deadly accidents of this scale are relatively infrequent.
Detectives said they were considering the possibility that the driver had been speeding down the slope, pointing to evidence of skid marks stretching for 30m at the scene.