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.
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 NTSB tweeted that it was "investigating today's crash of Pilatus PC-12 near Chamberlain, SD."
South Dakota is located in the Northern Plains, a region facing blizzard conditions as a storm blows eastward across the United States.
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"The men and women of law enforcement, first responders and medical professionals should be commended in their heroic actions to rescue the victims in extreme weather conditions," the state's attorney office said.