The Jamaican, who celebrates her 32nd birthday on Friday, is one of the greatest sprinters of all time and was the first woman to win a back-to-back Olympic sprint double when she retained both titles in Tokyo three years ago.
Thompson-Herah last competed in the 200m in April 2023 and sustained the injury during the 100m at the New York Grand Prix earlier this month as she finished in 11.48 seconds.
"It's never fun sharing news like this but at the New York Grand Prix, I felt something in the race and still insist to push, couple steps to the line I realise something is really wrong," the Jamaican wrote in an Instagram post.
"I sat on the ground because I couldn't apply any pressure to the leg whatsoever as I was carried off the track. I went quickly to get (a) medical check-up, and to find out that I have a small tear on my Achilles tendon.
"I got back home with a strong mindset to keep pushing and prepare for my national trials... but the leg wouldn't allow me to."
Thompson-Herah was also dogged by an Achilles injury after her astonishing sprint double at the 2016 Rio Olympics and she missed out on medals at the 2017 and 2019 world championships.
The three-times Diamond League winner stormed back with her second double at her second Games in Tokyo, also claiming a relay gold to take her tally to five.
Thompson-Herah said she would be cheering on her compatriots in Paris - hopefully on site - and was not giving up on her sprint career.
"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 wrote.
"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. I will be back."
Thompson-Herah had already decided not to defend her 200m title having missed the deadline to compete at the Jamaican Athletics Championships from June 27-30.
The athletics competition at the Paris Olympics takes place from August 1-11 at the Stade de France. The Games begin on July 26.
