Federer is seeking his fifth title in Hamburg, where he won his first tournament title in 2002 and broke into the top 10. The 17-time Grand Slam champion entered the event after his early elimination in Wimbledon.
Federer says Brands "can serve super and plays constantly" and vows not to underestimate the German.
Brands says he has "nothing to lose" and is going to "enjoy it." Like all seeded players, Federer had a bye into the second round.
Other winners included Spanish pair Albert Montanes and Roberto Bautista Agut.
Results from the ATP Hamburg Open (x denotes seeding):
First round:
Florian Mayer (GER) bt Nikolay Davydenko (RUS) 6-1, 6-3
Albert Montanes (ESP) bt Paul-Henri Mathieu (FRA) 6-4, 6-4
Daniel Brands (GER) bt Paolo Lorenzi (ITA) 7-5, 6-3
Jan Hajek (CZE) bt Lukasz Kubot (POL) 6-3, 6-2
Roberto Bautista (ESP) bt Alexander Zverev (GER) 6-3, 6-2
Dmitry Tursunov (RUS) bt Pablo Andujar (ESP) 6-7 (5/7), 7-6 (7/4), 6-2
Tobias Kamke (GER) bt Lukas Rosol (CZE) 6-3, 6-0