Civil aviation officials said the plane had taken off from Bogota's El Dorado airport just minutes before it went down yesterday in the Guaymaral neighborhood.
The city's police chief, Major General Humberto Gatibonza Carreno, told The Associated Press that the pilot and his three passengers died.
All 12 people injured were inside the bakery and were taken to hospitals with burns, the fire department reported.
It was the third crash of a small plane in Bogota in three months. Three people were killed in August when an aircraft crashed in the Cajica area, and three more died in October when a plane smashed onto a highway.