Forwards Thomas Muller and Mario Gomez are also doubtful with similar symptoms, coach Jupp Heynckes said before his Group A winners take on the English side having already secured their place in the last 16.
"After the last Bundesliga game I said Arjen Robben would start against City but obviously that's changed. I'd have liked to have played him after his long injury layoff as he needs games," Heynckes told a news conference.
"He trained well on Sunday, got the first symptoms of flu on Monday and then was ruled out today. He was obviously disappointed and so am I."
Dutch winger Robben, who is easing back after a groin operation, came on as a substitute in Saturday's 4-1 win over Werder Bremen in the Bundesliga and converted two penalties.
Despite being already through to the next round, Bayern had vowed to field a strong side against the Premier League leaders who need to win at home and hope Napoli fail to beat Villarreal in order to progress to the knockout stage.
"Obviously we were going to make one or two changes anyway but there may be forced changes so we'll wait and see what happens," Heynckes said.
"I think we'll have to wait until the final training session tonight and have a look [at Muller and Gomez] in the morning."
If City were hoping for an easy ride against a side with little to play for, Heynckes was quick to crush that notion.
"Tomorrow is a big match between two league leaders. Obviously it's a matter of prestige, there's also the question of the winning bonus and the UEFA rankings so it is an important match for Bayern Munich tomorrow," he said.
"My team will be performing on the pitch to win."
As four-times European champions, Bayern can offer plenty of advice to City's new kids on the block whose Champions League debut could well end with a group-stage exit on Wednesday.
"You need to get to know the Champions League for the positive and negative experiences," Heynckes said. "The Champions League is the top club competition... you get very close games and it is vital to gain that experience."
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