The top seed, who lost to Frances Tiafoe in his only match on the surface at Wimbledon last year, quickly found his range at the ATP 250 event, firing his forehand through the court in a rain-disrupted match to triumph against the #NextGenATP star after 72 minutes.
Tsitsipas has now recorded a Tour-leading 35 victories this season, highlighted by his run to the title at the Rolex Monte-Carlo Masters in April. His last win on grass prior to his victory over Stricker came against Frenchman Jeremy Chardy at the Cinch Championships in June 2019.
The Greek wild card is making his debut in Stuttgart and will next play former World No. 1 Andy Murray. It will be the second ATP Head2Head meeting between the pair, with Tsitsipas running out a winner in five sets at the US Open in 2021.
Tsitsipas reached finals in Rotterdam and Rome earlier this season, but arrived at the grass-court tournament in Germany off the back of a disappointing fourth-round exit at Roland Garros.
Stricker, who defeated Maxime Cressy in the first round, was facing a Top 10 opponent for the first time in his career. The 19-year-old won an ATP Challenger Tour title in Cleveland in February.