Assistant Commander Gary Lane said crews were first alerted to the incident just after 4.30pm by the building's fire alarm.
"At the peak of the fire there were 16 fire trucks in attendance. This evening 10 crews remain on site, alongside a number of support vehicles," Lane said.
"The fire is now contained but crews will remain on standby overnight."
The building was evacuated and no injuries were reported.
Epsom MP David Seymour, who was at the scene, said the building has been destroyed, and people who were staying there are trying to work out where they will go tonight.
"These are people who often don't have a lot and they are being taken, as I understand it, in a van by police to somewhere where they're going to try and help find accommodation from social services providers around the city, and I think it's wonderful the police are prepared to do that."
Seymour said some may have lost all of their possessions, and nearby residents have been offering food and clothing.
Police earlier said one person was arrested after they were called to a "disorder" at City Garden Lodge, in St George's Bay Road, just after 4.30pm, but the person has since been released without charge.
A scene guard will be in place overnight until a fire investigator can begin looking into the cause of the blaze.
Fenz is asking the public to avoid the area.
