Newspaper Der Tagesspiegel said the fire broke out in the stairwell of the building, where a stroller was allegedly torched after being doused in an accelerant.
The fire department said a man died from his injuries after jumping from the first upper story of the building on Sonnenallee. A woman and an infant were found dead on the same floor.
According to the daily Berliner Morgenpost, the baby was just nine days old.
Police said the victims were likely three family members. The fire reportedly began while residents were asleep.
Der Tagesspiegel said 20 others were taken to the hospital, some with signs of severe smoke inhalation.
A police spokesman described "dramatic scenes" at the site of the fire. Witnesses reported seeing panicked residents call for help from their open windows. Three people jumped from the building into an air rescue cushion set up by fire crews.
The blaze was brought under control at about 7 a.m. Two apartments were so severely damaged that they are no longer habitable. Sonnenallee, which is a major thoroughfare in the southern part of Berlin, was completely blocked off until midday Saturday.
The newspaper said the area around Sonnenallee has seen repeated arson attacks in recent years, involving prams set on fire in apartment hallways.