The 24-year-old forward started Friday's 3-0 win over Austria, assisting Toni Kroos' goal at the Allianz Arena, before making way for Julian Draxler before the finish.
However, he has since been diagnosed with a bout gastroenteritis and will return to Dortmund for treatment.
A statement from the German FA 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 in Torshavn, if Sweden fail to beat Kazakhstan in Astana.
In contrast, Lars Olsen's Faroe Islands side have lost all seven of their qualifiers.