The Bundesliga leaders lost 2-1 at the Mewa Arena, with Mainz star Lee Jae-sung grabbing a brace before Leroy Sane netted a consolation goal with three minutes to go.
It marked Bayern's second loss in four games - the matches they've had to cope without striker Kane.
The England captain had to be substituted in the first half of his side's 1-1 draw against Borussia Dortmund on December 1.
He was forced off with a knock, which has since been confirmed as thigh injury.
Manager Vincent Kompany recently confirmed Kane could return next week against RB Leipzig.
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However, in his absence, Bayern struggled in front of goal at Mainz.
Thomas Muller started up front, and Bayern failed to register a single shot on target throughout the clash until the final five minutes.
The German giants had coped okay without Kane in their previous two games without him.
First, they fired in four against Heidenheim in a 4-2 victory, before beating Shakhtar Donetsk 5-1 in the Champions League.
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But despite Michael Olise and Jamal Musiala starting for Bayern at Mainz, they struggled for fire power.
Kane has scored 20 goals in 19 games for Bayern in all competitions this season.
He scored 36 goals during his debut campaign in the Bundesliga last term, becoming the first English striker to win the prize since Kevin Phillips in 2000.
Manuel Neuer, left back Alphonso Davies and midfielder Joao Palhinha are other noticeable absentees for Bayern.
Bayern remain top of the Bundesliga, but their lead has shrunk to four points as Bayer Leverkusen won at Augsburg.
Mainz, meanwhile, have risen to sixth place.