The move means LeBron James will be the only representative of the NBA champion Heat available to play for the U.S. team in the upcoming games.
Bosh joined Dwyane Wade on the sidelines. Wade pulled out of the Olympics in order to undergo arthroscopic knee surgery.
Bosh's agent, Henry Thomas, told the South Florida Sun Sentinel that Bosh, who played on the 2008 Olympic squad, and his doctors agreed it would be prudent to "rest and rehab this injury so it does not become a chronic injury."
The final U.S. roster won't be announced until July 7.