Bosh missed nine games during the playoffs but returned to help Miami defeat the Oklahoma City Thunder in five games to claim the National Basketball Association title.
"I am extremely disappointed to say that due to injury I cannot represent my country in the 2012 Olympics in London," Bosh said in a statement.
"The abdominal injury I suffered in Game One of the Eastern Conference semi-finals is not fully healed."
Bosh's decision came one day after team mate Dwyane Wade announced he would be missing next month's Olympics to undergo knee surgery.
"Chris will be missed but we have to move on," said USA Basketball chairman Jerry Colangelo.
Bosh returned from the abdominal injury to play in the final three games of the Eastern Conference Finals against the Boston Celtics and competed throughout the NBA Finals.
He averaged 14.6 points and 9.4 rebounds a game during the NBA championship series win over Oklahoma City.
With Wade and Bosh out of consideration, there are 16 players left for 12 spots on the US team, down from an initial pool of 20.
One member of the NBA champion Heat remains on the roster that will begin training next week in Las Vegas, three-times league Most Valuable Player and NBA Finals MVP LeBron James.
"We've taken four bullets with the injuries to Rose, Howard, Wade and Bosh and it will now be a testimony to the infrastructure we put in with the national team roster. I feel very confident about our roster going forward," Colangelo said.
US coach Mike Krzyzewski said: "We're totally supportive of Chris and hope he recovers fully for his season next year.
"This opens up opportunities for other players in the pool to show their talents."
In the 2008 Olympics, Bosh averaged 9.1 points and 6.1 rebounds while shooting 77.4 percent from the field to help the U.S. win the gold medal.
Finalists for the US team include James, Carmelo Anthony (Knicks), Kobe Bryant (Lakers), Tyson Chandler (Knicks), Anthony Davis (University of Kentucky), Kevin Durant (Thunder), Rudy Gay (Grizzlies), Eric Gordon (Hornets), Blake Griffin (Clippers), James Harden (Thunder), Andre Iguodala (76ers), Kevin Love (Timberwolves), Lamar Odom (Mavericks), Chris Paul (Clippers), Russell Westbrook (Thunder) and Deron Williams (Nets).