The Pilatus PC-12, a single-engine turboprop plane, crashed shortly after take-off approximately a mile from the Chamberlain airport, the Federal Aviation Administration (FAA) said.
Among the dead was the plane's pilot, Brule County state's attorney Theresa Maule Rossow said, adding that a total of 12 people had been on board, AFP reported.
The three survivors had been taken to the hospital in Sioux Falls, she told US media.
The flight left the airport just before noon local time, with a destination of Idaho Falls Regional Airport in the western state of Idaho.
The FAA said investigators were en route to the crash site and that the National Transportation Safety Board (NTSB) would be in charge of the investigation.
The NTSB tweeted that it was "investigating today's crash of Pilatus PC-12 near Chamberlain, SD."