The 27-year-old US Open champion pinned his decision on the belief he would struggle to find his best form, having endured a tough 2021 season so far.
Thiem has lost his last three matches, including a first-round defeat to Pablo Andujar at the French Open, and has an overall 9-8 win-loss record for the year.
World number five Thiem confirmed, however, that he intends to play Wimbledon, which begins on June 28, and will then focus on getting in the best possible shape for his grand slam title defence at Flushing Meadows.
Nadal said earlier on Thursday that he would play neither Wimbledon nor the Olympics, where the tennis tournament starts on July 24, because he wished to recover from his clay-court season efforts.
Women's tour superstar Naomi Osaka has elected to miss Wimbledon but said on Thursday she would represent Japan at her home Olympics.
Thiem revealed his Olympics decision in a statement posted on his Twitter page, saying: "After talking with my team and analysing the situation I have taken the very difficult decision to withdraw from competing in the Tokyo Olympics.
"For me, like all athletes, taking part in the Olympics and representing my country is a huge honour and that makes this decision even tougher. However, 2021 did not start as expected and I don't feel ready to play my best in Tokyo.
"These last two weeks I have been training hard – and I’m starting to improve my conditioning and concentration little by little. My goal is to work hard the coming weeks, give my best at Wimbledon and keep training and hopefully defend my US Open title.
"I wish the entire Austrian team traveling to Tokyo all the best. I am young and I hope to be able to play for Austria at the Olympics in Paris 2024."