The man burst into the restaurant at 03:25 (08:25 GMT) in the suburb of Antioch and opened fire with a semi-automatic rifle.
Two other people were wounded. One of them wrestled the weapon from the man, who then fled the scene on foot.
Police are hunting for the suspect, whom they identified as Travis Reinking, 29, from Illinois.
He was arrested last year after entering a restricted area near the White House, Nashville police spokesman Don Aaron said.
James Shaw Jr, the customer credited with saving lives by seizing the gun from the killer, has told US media he does not feel like a hero because "it feels selfish".
Arriving in a pick-up truck, the killer shot two people outside the restaurant, before firing more shots inside, Mr Aaron said.
Three victims died at the scene and the fourth in hospital.
Police say he was naked except for a green jacket, which he shed as he left the scene.
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