The 24-year-old was substituted for Julian Draxler in Friday's 3-0 win over Austria, assisting Toni Kroos' goal at the Allianz Arena.
However, he is suffering from gastroenteritis and will return to Dortmund for treatment.
A statement from the Deutscher Fussball-Bund read: "Marco Reus will not fly with the German national team to the Faroe Islands.
"The 24-year-old (is) suffering from a gastrointestinal infection."
Germany remain unbeaten in Group C, having won six and drawn one of their seven matches, and can qualify for Brazil 2014 with a win, if Sweden fail to beat Kazakhstan in Astana.
Lars Olsen Faroe Islands side, conversely, have lost all seven of their qualifiers.
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