Two residents of the building in the center of the city have been taken to hospital. Others were treated at the scene by paramedics.
The fire brigade has cleared the entire complex. It concerns about 35 to 40 homes. It is not yet clear when the residents will be able to return home.
Mayor Petra Dassen-Housen of the municipality of Kerkrade, which includes Eygelshoven, announced on Twitter that the residents are being taken care of elsewhere.
The fire broke out on the third floor. It is a complex with mainly the elderly and vulnerable. The fire brigade responded with several fire vehicles. The fire is now under control.