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.
Duggar sisters unveil Christian dating rules in new book
LGBT community has 'bullied the American people': Bachmann