Thiem saved two set points in the first set of his 7-6 (5), 6-3, 6-0 victory over No. 2 seed Djokovic, who became the first man in nearly a half-century to claim a fourth consecutive major championship and completed a career Grand Slam in Paris last year.
The 23-year-old Thiem will next face nine-time French Open champion Rafael Nadal on Friday in his second straight Roland Garros semifinal appearance.
Nadal reached his record 10th French Open semifinal when fellow Spaniard Pablo Carreno Busta retired from their match early in the second set because of an injured abdominal muscle. The fourth-seeded Nadal led 6-2, 2-0 when No. 20 seed Carreno Busta stopped after 51 minutes of play.
Both matches were pushed to Wednesday due to persistent rain the day before in Paris.
Djokovic entered the day having dominated all five previous matches against Thiem, including in the French Open semifinals a year ago.
"All in all, it was decided I think in the first set," Djokovic said after the two-hour, 15-minute match. "I tried. I lost that crucial break in the beginning of the second (set), and he started serving better, backing it up with the first shot. He deserved to win. He was definitely the better player on the court today."
The Serbian's 12th Grand Slam title a year ago was the last time he won a major trophy. Djokovic had appeared in a record six consecutive semifinals in Paris.
Thiem, who was contesting his 250th tour-level match (156-94 record), now hopes to follow in the footsteps of 1995 Roland Garros champion and fellow Austrian Thomas Muster. Thiem has a 34-12 record on the season, second only to Nadal, who is now 41-6 overall in 2017.
"It's amazing for me," Thiem said. "To beat him for the first time in the quarters of the French Open is a dream."
Nadal is now 100-2 in best-of-five sets clay-court matches after reaching his 25th major semifinal with his victory over Carreno Busta.
Nadal, who celebrated his 31st birthday on Saturday, is 22-1 on clay this year, which includes three trophies at the Monte-Carlo Rolex Masters, the Barcelona Open Banc Sabadell and the Mutua Madrid Open.
"I'm playing well, I'm moving ahead," Nadal said afterward. "Thiem is a tough player. I hope that I won't lose. I won in Barcelona and Madrid, but I lost to him in Rome. ... If I play well, I hope that I will be able to book my spot in the final."
Thiem said of Nadal, "You have to play the best guys round after round. It's not getting easier on Friday."
The other men's quarterfinals later Wednesday were world No. 1 Andy Murray of Scotland vs. No. 8 Kei Nishikori of Japan, and 2015 champion and No. 3 seed Stan Wawrinka of Switzerland vs. No. 7 Marin Cilic Croatia.