Police in the state of Hesse said the victims, two women and a child believed to be nine or 10 years old, were standing at the edge of the airfield near Fulda when the accident occurred on Sunday afternoon.
Officials said the Cessna plane had been attempting to take off after an aborted landing manoeuvre, but lost power and failed to pick up.
The light aircraft then broke through a barrier, hitting the bystanders.
Emergency services were called to the scene shortly after 3.45pm.
Three passengers on board the plane were treated for light injuries and an eyewitness was treated for shock, according to Hesse’s public broadcaster, Hessischer Rundfunk.
The 56-year-old pilot was unharmed.
The plane came from the Mannheim area of southwestern Germany and had been on an excursion to the Wasserkuppe mountain area.
Wasserkuppe is popular with paragliders and light aircraft enthusiasts, according to German media. Hillwalkers and other visitors also visit the area.
Additional reporting by agencies
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