A spokeswoman for Greyhound, quoted by the Associated Press, said the company had suspended all its bus services nationwide as a precautionary measure. About 1,900 of its 2,300 buses were on the road at the time.
A passenger told Nashville's WTVF television that the crash occurred after a man walked up to the front of the bus and slashed the driver's throat.
The bus then swerved off the road and crashed, she said.
Tennessee officials later confirmed that the driver had been attacked. The bus then flipped onto its side, and ended up in a ditch.
The incident happened near Manchester, halfway between Nashville and Chattanooga, on Interstate 24.
The man who allegedly caused the crash is still alive, according to US Justice Department spokeswoman Susan Dryden. He holds a Croatian identification card, she said.
There is no suggestion yet that the incident was linked to the 11 September terror attacks on New York and Washington. The US Transportation Department said it appeared to be a "random" event unrelated to those attacks.
Agitated assailant
The witness, identified as Carly Rinearson, said the assailant, aged 30 to 35, had repeatedly approached her front seat in the bus and asked what time it was.
The man then asked if he could have her seat, and after she refused he attacked the driver.
Steve DeFord, a spokesman for the Coffee County Sheriff's Department, said "the assailant" was among those killed and that the investigation had been turned over to the FBI, which rushed agents to the scene.
Greyhound said buses currently on the road would be allowed to reach their destinations but all other planned journeys had been suspended.
Greyhound travels to some 3,700 destinations and makes nearly 20,000 departures a day.