Federer, seeded third this year, ousted Adrian Mannarino 6-4, 6-2. He won nearly three-quarters of the points on serve, even with a dropped service game. He finished off four of his 13 break points.
Federer is a five-time winner of the Swiss Indoors, which is played in Basel where he was born in 1981. His most recent title was in 2011. He was the runner-up last year to Juan Martin del Potro, who is the top seed in the event this year.
The other three first-round matches on Monday's schedule were also finished off in straight sets.
Lukasz Kubot took out Daniel Gimeno-Traver 7-6 (8-6), 6-2, getting three breaks to take the second set.
Tobias Kamke and Alexandr Dolgopolov both won by 6-4, 6-4 scores. Kamke topped Victor Hanescu by saving 7-of-8 break points he faced. Dolgopolov needed only 57 minutes to post his win over Kenny De Schepper. Dolgopolov dropped only 10 points on serve.