A home behind the sports field was damaged, but no injuries on the ground were reported, Atlanta Fire Rescue Sgt. Cortez Stafford said.
The plane's wreckage was spread out on the field over about 100 yards (90 meters), he said.
The aircraft was "shooting out of the sky," witness Reggie Dumas told reporters at the scene.
"As it was going down, you could see the wings shifting back and forth," said Dumas, who saw the aircraft plunge as he drove along a nearby road. He said he jumped out of his car to see if he could help anyone, but saw no survivors — only smoke.
The plane was a Cessna Citation V jet, Federal Aviation Administration spokeswoman Kathleen Bergen told The Associated Press.
The plane was headed to the Millington-Memphis Airport when it went down, airport Executive Director Roy Remington said.
Remington said a fire official at the Millington airport, located about 20 miles (32 kilometers) north of Memphis, was working with authorities in Atlanta to determine the identities of those killed. Remington says the victims were believed to be from the Memphis area.
"This is a tragedy," he said.
The jet had departed from a runway at nearby Fulton County Airport-Brown Field and went down about 1.5 miles (2.4 kilometers) east of the airport shortly after noon, Bergen said. The airport itself is about 10 miles (16 kilometers) west of downtown Atlanta.
Firefighters had to make their way through jet fuel to put out the flames on the football field, Stafford said.
The airport is a busy general aviation facility with an air traffic control tower and fire station. It averages a combined 164 takeoffs and landings each day.
The National Transportation Safety Board said it is investigating the crash.
Associated Press reporters Adrian Sainz in Memphis and Chevel Johnson in New Orleans contributed to this report.