Bayern have already lost twice to Gladbach this season in the German league and memories of their 3-1 away defeat in January are still fresh in the memory, but Saturday night's draw gives them the chance for revenge.
Munich, who face FC Basel in the Champions League Round of 16 on February 22, will return to Gladbach on March 21 for the semi-final with a place in the German Cup final at Berlin's Olympic Stadium on May 12 up for grabs.
German league leaders Borussia Dortmund face second division side Greuther Fuerth in the other semi-final.
The Bavarians minnows have already beaten German league teams Nuremberg and Hoffenheim on their way to the last four.
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