A 62-year-old man, who police say was the boyfriend of the woman, 42, has been arrested in connection with the case.
At around 1.50am, the the authorities received a report of a dispute at the sub-divided flat in Tai Po. At about 2.02am, there was a report of black smoke billowing out of the unit, police said.
The force said the three alleged victims were found unconscious inside the flat with multiple injuries, with the mother having suffered some 40 knife wounds.
First responders found the man in a half-conscious state on a rear staircase in the building.
He was said to be in a critical condition in hospital.
Acting superintendent Fan Wai-ho said the four people lived together in the flat.
“We believe the two adults had a dispute because of relationship problems. The suspect then allegedly attacked the woman with a sharp object. The two girls were also injured probably because they tried to stop the attack,” Fan said.
A fire was started in the unit after the attack, Fan added.
Authorities said the fire didn’t spread to other flats, but about a dozen people were evacuated from the building.