In his place Saturday, Hector Sanchez went 1-for-4 with a walk-off home run in San Diego's 5-3 victory over the Giants.
"That was as loud as I'd seen somebody get hit," Green said of the foul tip off Hedges' mask. "That night, he said he felt fine and was feeling relatively fine the next morning until he got up and started doing a bunch of activity and just doesn't feel quite right.
"With that, you always want to be cautious as a manager and make sure you put a guy in a position to protect his long-term health and his career, so we'll be cautious with him, make sure he feels great before he's back out there."
Green said doctors have classified the injury as "subconcussive," meaning it is below the level of a concussion. Hedges hit in the cages before Sunday's game.
This is the second time in eight games Hedges has missed time due to an injury.
After missing consecutive games against the Indians with a stiff neck, Hedges returned in the Padres' series opener against Philadelphia and blasted a pair of homers on July 7, adding a game-winning sacrifice fly.
Hedges' 13 home runs led National League catchers entering play Sunday.
"We were hopeful coming into today that we'd be able to get him back out there, but [he] doesn't feel remarkably better," Green said. "We're hopeful it's nothing serious and it's just a couple days and he clears up and feels fine."
● Right-hander Carter Capps, pitching with Triple-A El Paso, has returned from a twisted ankle as he continues to work his way back from Tommy John surgery. Green initially deemed the injury "not minor" when Capps was put on the Minor League disabled list July 4, but Capps returned Friday and pitched a perfect inning for El Paso.
"He's as tough as anybody," Green said.
● Outfielder Travis Jankowski, recovering from a right foot fracture, played in an Arizona League game Saturday, playing center field, getting two at-bats and scoring a run.
● After a couple of days off, rehabbing left-hander Buddy Baumann (left shoulder soreness) is expected to pitch in consecutive games with Double-A San Antonio. If all goes well, he will be activated shortly after that, Green said.