Thick white smoke was billowing out of the building on Ninth Avenue near West 47th Street around 11 a.m.
The fire broke out on the first floor of a building and moved up to the second floor.
The FDNY said 106 firefighters and EMS responded, and 25 units were deployed to help get the blaze under control.
Three civilians and three firefighters were treated for non-life threatening injuries.
One person suffered a minor injury and was treated at the scene, police said.
The cause of the fire is under investigation.