Braves spokesman Brad Hainje said Thursday that Salazar underwent surgery Wednesday night and "he's having more surgery today."
Hainje said "it may be another day or two before we have final clarification on everything they had to do.
A Braves spokesman told multiple media outlets on Wednesday that Salazar didn't sustain any brain damage but suffered multiple facial fractures. He will have to undergo testing to determine damage to his left eye.
"We feel very fortunate and blessed that Louie is alive and that he is responding and able to communicate with his family and talk," Braves general manager Frank Wren told reporters Wednesday. "We just pray for the best as he continues these tests and evaluations and whatever else is ahead of him. "
Wren said Salazar was unconscious when an ambulance drove onto the field in the first inning to help the 54-year-old former big leaguer. Wren said Salazar was hit around the nose, toward his left eye.
Salazar was struck while standing on the top step of the first-base dugout. The Braves said Salazar's son, who was at the game, and his wife, who was not in attendance, also went to the hospital.
Chipper Jones was on first base when the accident occurred. He said Salazar was leaning against a dugout railing and toppled backward, hitting his head on the concrete floor.
"There were two things," Jones said. "First he got hit, then he fell backward and hit his head on the floor of the dugout. It was bad enough when he got hit but worse when he hit the floor."
Salazar played in the major leagues from 1980 to 1992 for the San Diego Padres, Detroit Tigers, Chicago Cubs and Chicago White Sox. He mostly played third base, was a career .261 hitter with 94 home runs and played in the 1984 World Series for the Padres.
Salazar was set to manage the Braves' Class A team in Lynchburg, Va. He was the Double. A hitting coach for the Los Angeles Dodgers the past three seasons.