Another 10 people were missing and seven people were found alive, the rescue workers said.
The building fell at around 10:30 a.m. local time in the middle-class neighborhood of Dionisio Torres.
Television footage showed a handful of rescuers in orange suits digging through a massive pile of wreckage in a middle class area of Fortaleza, the capital of Ceara state.
According to G1 news website, pedestrians who were passing by the building when it collapsed were taken to nearby medical clinics, and access to streets surrounding the wreckage was closed by authorities.
In April, two buildings caused the death of a dozen of people in the western neighborhood of Itanhangá, a militia-controlled outer borough of Rio de Janeiro, exposing the issues of housing in poor shanty towns.