The building at the intersection of 4th Avenue and Ash Street first caught fire sometime around 1:30 a.m. PT.
According to unconfirmed reports some people walking past spotted the flames and alerted the residents inside.
So far no injuries have been reported, but the building appears to be completely destroyed.
Residents of neighbouring buildings have been evacuated but firefighters have apparently stopped the flames from spreading.
Traffic has been shut down for several blocks in the area.
Firefighters from Delta and Burnaby were called in to help New Westminster firefighters fight the blaze.
By 6 a.m. much of the building had collapsed by firefighters appeared to have the blaze under control.
Google Map: 4th Ave and Ash St, New Westminster
YouTube: Huge apartment fire in New Westminster