It is unclear what caused the blaze, which broke out shortly after midnight local time and took firefighters several hours to bring under control.
Firefighters and airport police were among the injured, Dutch media reported.
The detention block is mainly to hold suspected drug traffickers, Dutch police officials said, although it is also used to hold illegal immigrants before expulsion.
The identities of the dead have not been released.
Approximately 350 detainees were being held in the block at the time of the fire.
Following the fire prisoners were transferred to other facilities or moved to undamaged sections of the building.