Crews were called to the unit block of Boyds Valley Drive at about noon.
Four people were treated by paramedics at the scene and were taken to Christiana Hospital.
A 60-year-old man was treated for facial burns and a 43-year-old man, a 41-year-old woman and a 3-year-old girl were treated for smoke inhalation. All four people were listed in stable condition.
The Delaware State Fire Marshal is investigating the incident.