Nadal, the world number five and defending champion, failed to convert a match point at 5-4 in the final set.
The nine-time French Open winner is top seed for a tournament in Rio de Janiero next week that also includes British number two Aljaz Bedene.
Thiem, 22, will be looking for his first ATP singles title of the season in Sunday's final.
"It was a tough match. I had a chance to win and missed it but Thiem played well," said 29-year-old Nadal, who has won 47 titles on clay.
"I'm not worried. I just lacked consistency and need to make fewer unforced errors, but that's nothing."
Thiem will face Nicolas Almagro in Sunday's final after the Spaniard came through 6-4 7-5 against compatriot David Ferrer, who had earlier played a rain-delayed quarter-final against Pablo Cuevas.
