The 22-year-old bounced back from losing his opening round-robin match against Novak Djokovic by defeating Cameron Norrie and Andrey Rublev.
The Serbian went 27-1 in major championships this year, winning titles at the Australian Open, Roland Garros and Wimbledon.
Day 1 also features second seed Daniil Medvedev and eighth seed Casper Ruud against French veterans Richard Gasquet and Jo-Wilfried Tsonga, respectively.
The Greek star squandered two match points in the second set but still managed to earn a spot in the last four in Cincinnati.
Spaniard Carreno Busta eased past Filip Krajinovic in straight sets to win the Hamburg European Open title.
The second seed survived a tie-breaker in the first set before running away with the match in the second to set up a final date with Filip Krajinovic.
Thiem was leading the opening set 5-2, but appeared to injure his right wrist when he struck a forehand. Elsewhere, Daniil Medvedev had it easy in his match.
Canada's Denis Shapovalov announced his that he would not be taking part in the French Open 2021 due to a shoulder injury.
Third seed Ruud beats Denis Shapovalov in straight sets to win the Geneva Open final, while John Peers and Michael Venus capture the doubles title.
Denis Shapovalov will take on Casper Ruud in the Geneva Open final after both won their semi-final bouts in straight sets wins on Friday.