The German spoiled former world number one Federer's return to the tournament after nine years with a shock 6-3, 6-4 second round upset.
Federer, who saved two match points before going down, had laboured for three sets a week ago in Hamburg to beat Brands.
World number five Federer has won only the Halle title this season after claiming his 17th Grand Slam title at Wimbledon in 2012.
Last week, the 31-year-old was stunned by Argentine qualifier Federico Delbonis, the world number 114, in the Hamburg semi-finals.
That defeat came just a month after Federer was knocked out of Wimbledon by Ukraine's world number 116 Sergiy Stakhovsky in the second round.
That brought to an end a run of 36 consecutive Grand Slam quarter-final appearances for the Swiss.