Thompson-Herah, who completed the 100m-200m gold medal double at both the 2016 and pandemic-delayed 2020 Olympics, confirmed her decision after pulling out of this week's Jamaican trials.
"I am hurt and devastated to be missing the Olympics this year but at the end of the day it's sports and my health comes first," Thompson-Herah, 31, wrote in a statement shared on social media.
Thompson-Herah had already abandoned her bid to defend her 200m crown in Paris after opting not to take part in the 200m at this week's Jamaica trials in Kingston.
However, she had entered the 100m at the trials and retained hope of being able to compete in Paris over the shorter distance.
Thompson-Herah's fitness had been in doubt ever since she competed at a race in New York earlier this month, where she needed to be carried from the track after suffering a torn Achilles.
In her statement on Wednesday, Thompson-Herah said she realised the injury was serious immediately.
"I sat on the ground because I couldn't apply any pressure to the leg whatsoever as I was carried off the track," Thompson-Herah wrote.
A medical examination later revealed a "small tear" of the Achilles tendon, she said.
"Funny enough I got back home with a strong mindset to keep pushing and prepare for my national trials another shot of my third Olympics but the leg wouldn't allow me to," she said.
Thompson-Herah insisted, however, that she plans to continue her sprinting career despite her Olympic heartbreak.
"It's a long road but I am willing to start over and keep working and to make full recovery and resume my track career," she said.
Although Thompson-Herah has never won an individual sprint gold at a world championships, she has dazzled in the Olympic arena.
Her 100m personal best of 10.54sec -- set in Eugene, Oregon in August 2021 -- is the second fastest time in history, second only to Florence Griffith-Joyner's 1988 world record of 10.49sec.
