No one on the ground was injured, officials said.
The twin-engine Beechcraft 55 had taken off from the nearby DeKalb-Peachtree Airport and was headed to Venice, Florida, said FAA spokesman Christopher White. He said he did not know if there had been a distress call from the plane.
Witnesses said the plane spun out of control.
``It was tumbling straight down,'' said Malcolm Okosun, who saw the plane while working on a construction project about a block from the downtown crash. The plane hit the shop in a ``straight-down nose dive,'' he said.
The plane ended up afire in the building's parking lot. Parts of the building were blackened but there was no apparent structural damage.
Only a few people were in the building and none needed medical attention, said Fire Department spokeswoman Sandra Walker.
A rainstorm was moving through the city at the time of the crash.
The crash happened in the city's historic Sweet Auburn neighborhood, where King grew up and preached at Ebenezer Baptist Church _ only a few blocks from the crash site. His birthplace is only about 40 yards (37 meters) away.