The four police officers and the vehicle's driver have been taken to a local hospital.
The injuries are serious, but not life threatening, according to the Vancouver Police department.
The Fatburger restaurant is located on Denman Street near Davie Street.
Multiple police cars and ambulances have blocked off Denman Street, tweeted CBC's Meera Bains from the scene.
Police are looking for witnesses and ask anyone with information to approach an officer or call 604-717-3321.