Gauff, who reached the last-16 stage at Wimbledon before losing to Angelique Kerber, has passed the $1million mark for prize-money in a season for the first time this year, rising to 25th in the WTA rankings.
The 17-year-old has a win-loss record of 31-12 for the campaign so far, and won the Emilia-Romagna Open title on clay in May.
She announced her news on social media, writing: "I am so disappointed to share the news that I have tested positive for COVID and won't be able to play in the Olympic Games in Tokyo.
"It has always been a dream of mine to represent the USA at the Olympics, and I hope there will be many more chances for me to make this come true in the future. I want to wish TEAM USA best of luck and a safe Games for every Olympian and the entire Olympic family."
The United States Tennis Association said it was "saddened" by the news, adding: "The entire USA Tennis Olympic contingent is heartbroken for Coco.
"We wish her the best as she deals with this unfortunate situation and hope to see her back on the courts very soon. We know Coco will join all of us in rooting on the other Team USA members who will be travelling to Japan and competing in the coming days."
Gauff joins a host of star names from tennis who have been ruled out, or have ruled themselves out, of the trip to Tokyo.
Serena Williams decided she would not play even before suffering a leg injury at Wimbledon, while Simona Halep, Sofia Kenin, Victoria Azarenka, Bianca Andreescu and Kerber are among other major absentees from the women's draw.