Schweinsteiger picked up 92 out of 527 votes with Ribery on 87 and Mueller on 85.
"I'm a little surprised to be fair. There were times when certain articles were mostly critical of me," he told Kicker.
Treble winners Bayern provided nine of the top 15 players in the award with Bundesliga runners-up Borussia Dortmund filling five of the remaining berths.
Only Bayern Leverkusen centre-forward Stefan Kiessling, who was the league's top scorer last season with 25 goals, managed to break up the top two's hegemony.
Now-retired Jupp Heynckes, who led Bayern to the Champions League, Bundesliga and German Cup last season, was a run-away winner in the coach's award.