كتب : وكالات
The Bavarian giants, who clinched the domestic double last season, dominated the game but could not find a way past the Cologne defense.
Cologne's Colombian keeper goalkeeper Farid Mondragon, 39, produced an outstanding display to thwart Bayern forwards.
Bayern extended their winless streak to three matches, having secured just one win in four games.
They lie ninth in the 18-team league table with five points.
VFB Stuttgart claimed their first points of the season in an emphatic fashion after routing Borussia Monchengladbach 7-0.
The five-time German champions, who lost their first three league games, were helped by a hat-trick from Russian striker Pavel Pogrebnyak.
Mainz 05, who defeated Werder Bremen 2-0, are the only team to claim maximum points.