Fire-Rescue spokesman Don Delucia says the crash happened Wednesday morning at Palm Beach County Park Airport in Lantana.
He says it appears the plane lost power and was making an emergency landing when it struck the parked plane.
The impact caused the landing plane to spin around and come to a rest underneath a storage trailer.
No one on the ground was injured. The cause is under investigation.
WPEC-TV footage showed the wreckage of a red section of plane tail by the trailer. Fire trucks were parked nearby on the tarmac.