Defender Lahm, who played in Bayern Munich's 2-0 win over Schalke 04 on Sunday, will remain in Munich for treatment, the DFB said in a statement.
Bender, whose twin brother Lars has also been called up for the match, sustained the injury in Borussia Dortmund's 3-1 win over Hannover 96 on Sunday.
"Initial fears for a broken nose have not been confirmed but he has a major bruise on the bone there," Germany coach Joachim Low told reporters.
"So it is understandable that he called his participation off as he would be unable to go into one-on-one situations."
Bender has been in outstanding form for champions Dortmund this season, helping them to a four-point lead over second-placed Bayern Munich.
Twin Lars said it was a shame they would not be on the pitch together for the first time for Germany.
"I was looking forward to our first joint appearance and am sad it will not work out this time. But it can still happen," the Bayer Leverkusen player told reporters.
Low said he would not replace Bender in the squad, or captain Philipp Lahm who pulled out on Sunday with a knee injury.
"This match is the end of a string of tests since 2010," said Low. "We have consciously picked top opponents and in all those games we used more than 20 players without seeing major changes in our form. That means we have a balance in each position."
Three-time European champions Germany, without a title since 1996, are among the favourites for this summer's Euro 2012 finals in Poland and Ukraine after qualifying top of their group without dropping a point.
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