Police spokesman Paul J. Browne said the man being questioned lived in the building.
Investigators were looking at several possible motives for the arson.
The fire early Saturday was the city's deadliest since a 2007 fire killed 10 people, nine of them children, in the Bronx.
The Brooklyn fire is believed to have started near the front door. Fire Commissioner Salvatore Cassano said accidental fires don't usually spark behind front doors, where there are few electrical sockets or other potential fire hazards. Tests for accelerants were incomplete.
Four men and a woman, all Guatemalan immigrants, died in the blaze. Luisa Chan, the only victim identified so far, and her husband, Miguel, who escaped, tried to lower their 2-month-old daughter, Maria, out of a window in a car seat, but the baby fell out and suffered a fractured skull. She remained in critical condition but was expected to survive.
Their 2-year-old son, Josias, survived.
The families of the other victims had not been officially notified.
The fire started around 2:30 a.m. Saturday and quickly engulfed the three-story building, consuming a ground-floor Japanese restaurant and two apartments on the upper floors. The stairwell between the floors collapsed, as well as part of the roof, trapping residents.
As many as 20 people lived in the building, which did not have adequate smoke detectors, officials said.
