The Germany international took 92 votes in a poll conducted by Kicker magazine among 527 sports reporters.
Ribery received 87 votes and Muller took 85 while former Bayern boss Jupp Heynckes was the overwhelming winner of the best coach award with 383 votes, ahead of Freiburg's Christian Streich with 77.
"This title is also for the team," said Schweinsteiger, who was somewhat taken aback by winning.
"It surprises me a bit because there were times when a lot of critical things were reported about me."
The 28-year-old will receive his award prior to Bayern's opening Bundesliga game of the season against Borussia Monchengladbach on August 9.
Only Stefan Kiessling was able to break into a top 10 otherwise dominated by players from last season's Champions League finalists Bayern and Borussia Dortmund, who also met in the German Supercup on Saturday night.
Speaking of his award, Heynckes, who led Bayern to an historic treble before stepping aside, said: "This rounds all of this fairytale off. Many dreams became reality."