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, Fla., 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. "It looked like there was some pretty heavy wind," said Chris Spanovic, who watched the plane go down from two blocks away.
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 away.
The neighborhood, which dubs itself as the cradle of the civil rights movement, includes old warehouses that have been converted into apartments and businesses.
The plane was registered to J&R Aircraft Inc. of Nokomis, Fla., according to an FAA database. There was no telephone listing for the company. Officials at both the DeKalb-Peachtree Airport and the Venice Municipal Airport in Florida said they had no information about the plane.
By Kristen Wyatt