The building, like many apartment structures in Oakland, has a long and recent history of code violations.
Battalion Chief Erik Logan did not provide the gender of the deceased.
Three people who were rescued were injured.
The fire is at the intersection of San Pablo Avenue and Mead Avenue in Oakland, according to fire officials.
Residents also included a 9-year-old boy who escaped in his underwear and socks.
Authorities in California fear at least one person is dead after an early morning four-alarm fire swept through a residential building in Oakland. Firefighters said they thought they saw a body on the third floor, but officials have not confirmed a death. A tweet posted minutes later said crews were withdrawing from the building because the floors and roof were compromised.
The television station reported that seven people were rescued and as many as 60 people may have lived in the building.
Last December, 36 people were killed when a fire erupted at a dance party at a sprawling, two-store warehouse in Oakland known as the Ghost Ship that had been leased to an artists' collective.