Five people, including two Iranian police officers, were killed. Others were trapped under the rubble resulting from the collapse.
A residential building collapse in Brazil on Friday caused 14 deaths.
Firefighters were continuing to tackle the blaze and 80 people have been evacuated, according to the rescue services.
While Israel finally issued a serious earthquake standard for new construction in 1988, the older buildings which often sit on skinny columns are sitting ducks.
The collapse of a building in Aleppo and the 5-year anniversary of the invasion of Afrin are symbols of how Syria continues to suffer while the global powers concentrate elsewhere.
The five-story building in the Sheikh Maksoud district of Syria's second-largest city collapsed due to water leakages that weakened its foundation.