A statement from the PGA Tour confirmed the 2020 US Open champion failed the final testing protocol before heading out to the Japanese capital to represent Team USA.
In his place comes Patrick Reed, who is undergoing testing on Sunday and Monday before departing for Japan.
Should he clear that hurdle Reed will become a two-time Olympian having also competed at Rio 2016. He joins Justin Thomas, Open Championship winner Collin Morikawa and Xander Schauffele as part of a star-studded USA line-up in the men's event.
"I am deeply disappointed not to be able to compete in the Olympics for Team USA," said DeChambeau.
"Representing my country means the world to me and it is was a tremendous honour to make this team.
"I wish Team USA the best of luck next week in Tokyo. I will now focus on getting healthy, and I look forward to returning to competition once I am cleared to do so."
Reed added: "I am so excited to have the opportunity to represent our country and be a part of Team USA in Tokyo.
"I wish Bryson nothing but the best, and I know how disappointed he is to not be able to compete, and I will do my best to play my best and represent our country."
The Spanish Olympic Committee announced the world number one had returned a positive result on his third PCR test after competing at The Open at Royal St George's, having previously recorded two negative outcomes ahead of his appearance at the Games.
American Bryson DeChambeau was also ruled out of competing for the same reason on Sunday, having not yet travelled to play in Japan.
For Rahm, it is the second time he has tested positive in as many months. He had to withdraw from the Memorial Tournament on the PGA Tour when leading by six shots after 54 holes.
The 26-year-old won the U.S. Open upon his return to action, securing the first major of his career by one shot thanks to a birdie-birdie finish on a dramatic Sunday at Torrey Pines.
With a shortage of time and considering the health protocols in place for the Olympics, a replacement will not be selected. Spain still has one competitor left in the field in Adri Arnaus, the world number 166.
As for DeChambeau, he admitted to being "deeply disappointed" at missing out on Tokyo.
"Representing my country means the world to me and it is was a tremendous honour to make this team," he said in a statement released by the PGA Tour.
"I wish Team USA the best of luck next week in Tokyo. I will now focus on getting healthy, and I look forward to returning to competition once I am cleared to do so."
Patrick Reed will replace him, provided he clears coronavirus tests scheduled on Sunday and Monday before departing for Japan.
