The Italian struggled with illness during his Wimbledon quarter-final loss to Daniil Medvedev earlier in July.
Sinner was one of the favourites for the gold medal on the Paris clay, reaching the French Open semi-finals after winning his first major title at the Australian Open in January.
“After a good week of clay training I started to feel unwell,” the 22-year-old posted on X.
“I spent a couple of days resting and during a visit the doctor found tonsillitis and strongly advised me against playing.
“Missing the Games is a huge disappointment as it was one of my main goals for this season.”
The tennis tournament takes place from 27 July to 4 August.
Sinner had been due to play singles and doubles at Roland Garros.
His withdrawal means that Novak Djokovic will be the top seed in the singles when the draw is made on Thursday.
A number of players will miss the Paris Games, either through illness or injury.
Marketa Vondrousova, silver medallist in Tokyo three years ago, pulled out on Tuesday with a hand injury, while Polish world number seven Hubert Hurkacz also withdrew.
Other notable absentees include Britain’s Emma Raducanu, world number three Aryna Sabalenka and two-time Wimbledon runner-up Ons Jabeur.
But Djokovic, Wimbledon champion Carlos Alcaraz and US Open winner Coco Gauff are all slated to play.
The Olympics take place just 13 days after Wimbledon ended and finish three weeks before the US Open begins.
The Olympic tennis competition consists of men’s and women’s singles and doubles, as well as the mixed doubles.
Andy Murray is set to compete for Great Britain as he ends his playing career, with Dan Evans, Jack Draper and Cameron Norrie also in Paris in singles.
Murray will play doubles with Evans, while Joe Salisbury and Neal Skupski are real medal contenders in the same event.
Katie Boulter is the sole British representative in the women’s singles and will play doubles with Heather Watson.
Watson and Salisbury will also compete in the mixed doubles.