Police issued a murder warrant for Reinking late Sunday morning.
Little information has been released by authorities about Reinking, who is from Morton, Illinois.
Police said Reinking sat in his truck in the Waffle House parking lot for about four minutes before getting out of the vehicle and killing two people outside the restaurant around 3:25 a.m. He went inside the Waffle House and continued to shoot, killing a third person.
A fourth person died after being taken to Vanderbilt University Medical Center in Nashville, police said.
Related: Waffle House shooting: Remembering the victims
This is the second shooting to occur in the Antioch area in less than a year. In September, one person was killed and seven others were injured when a gunman opened fire at the Burnette Chapel Church of Christ. The church is located less than two miles from the Antioch Waffle House.
Police spokesman Don Aaron said at least seven people were taken to a hospital for treatment after Sunday’s shooting. Two people suffered minor injuries and were released from Southern Hills Medical Center, a hospital spokesman said. Police also identified Reinking after the pickup truck he allegedly drove to the restaurant in was registered to him.
Aaron said police retrieved an Illinois driver’s license that identified Reinking.
He added that Reinking was known to law enforcement in Illinois and in the federal system.
Morton is a town of 16,000 people in central Illinois, located several miles southeast of Peoria.