Police were called to the apartment shortly after 10.30 a.m. PT after receiving reports of a small child crying, a man yelling and blood on the walls of the apartment building hallway.
On arrival, a man challenged police with a weapon, and was shot and injured by officers, the VPD said in a statement.
A woman, with apparent multiple injuries was declared dead at the scene, and a girl of around five or six was taken to hospital with injuries.
According to a neighbour, one attending paramedic who described the scene as a "blood bath", said the victim had been stabbed many times all over her body.
Police said the suspect was transferred to hospital.
The incident is Vancouver's third homicide of 2014.