It is unclear when Posey, 32, suffered the concussion. The six-time All-Star caught all of Tuesday's 14-4 win over the Colorado Rockies.
This is Posey's second career stint on the concussion injured list. He missed seven games with a concussion in April 2017.
The Giants also placed southpaw starter Drew Pomeranz on the 10-day injured list with a back muscle injury. Catcher Aramis Garcia and right-hander Tyler Beede have each been recalled from Triple-A Sacramento.
Posey is hitting a career-low .245 with two home runs and 13 RBI in 32 games this year. The three-time World Series champion recently had a nine-game hitting streak and hit his second home run of the season against Reds ace Luis Castillo on Sunday afternoon.
The Giants already are without veteran backup Erik Kratz, who was placed on the injured list with a left hamstring strain last Friday. Backup Stephen Vogt will likely split time behind the plate with Garcia.