Thiem, the youngest player in the ATP's top 20 at age 22, was about the only bright spot on a rain-soaked day that saw the match between No. 2 seed David Ferrer and fellow Spaniard Albert Ramos-Vinolas rained out.
Much of the rest of the playing schedule was also washed out in the third straight day of rain in Rio de Janeiro.
Thiem, the No. 5 seed, had his problems with the rain, too. He took the first set and got to 3-3 in the second when a downpour hit. He had to wait for over an hour to finish the match.
"It was not very nice to go into the rain delay because I almost had the match," Thiem said.
Thiem won on clay in Buenos Aires last week and beat the king of clay, Rafael Nadal, in the semifinals. He then defeated another Spaniard Nicolas Almagro in the final for his fourth ATP singles title, all on clay.
"These are exactly the matches I need to improve," Thiem said. "I saw last week that I can beat the big guys."
Tsonga has had a tough week in Brazil. His doubles match was rained out on Monday, and his singles match against Monteiro was rained out on Tuesday.
"It was good for me to be here," Tsonga said. "It was good experience for me anyway, even if it was difficult for me."
Nadal, the top seed, plays Almagro on Thursday in the second round, and Ferrer will face Ramos-Vinolas.
On the women's side of the combined ATP-WTA event, fifth-seeded Polona Hercog of Slovenia was beaten 7-5, 7-6 (3) by Sorana Cirstea of Romania in a second-round match.