The Bayern Munich pair have been forced to isolate and will leave their team hotel, the German Football Association (DFB) announced on Wednesday.
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Hoffenheim keeper Oliver Baumann has been called up as a replacement while Wolfsburg midfielder Maximilian Arnold has also been drafted in.
Borussia Dortmund's Julian Brandt has also left the camp with a non-Covid related illness.
A statement from the DFB read: "Leon Goretzka (27) and Manuel Neuer (36) tested positive for the Coronavirus on Wednesday morning.
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"Both national players from FC Bayern Munchen were isolated, and will leave the team hotel. Due to a positive coronavirus test within one of the players' private circles, the medical team conducted a rapid antigen test on the whole national team.
"All members of the coaching staff and the team are required to test negative before travelling. Confirmed contacts of both players will be tested daily."
Germany host Hungary in Leipzig on Friday before travelling to Wembley to face England next Monday.
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