Both Bayern Munich players were isolated after the positive results and have since left the team hotel in Gravenbruch, near Frankfurt, the German soccer federation said on Wednesday.
They will miss the Nations League games against Hungary in Leipzig on Friday and England in London on Monday.
“The alarm bells are going off,” national teammate Jonas Hofmann said. Players who had contact with Goretzka and Neuer were to be tested daily for COVID-19.
Germany coach Hansi Flick called up Hoffenheim goalkeeper Oliver Baumann as a replacement for Neuer, though Barcelona’s Marc-André ter Stegen is likely to play against Hungary. He later also called up Wolfsburg midfielder Maximilian Arnold to compensate for Goretzka’s absence.
Goretzka and Neuer were at the Oktoberfest beer festival with the rest of the Bayern team on Sunday. All Germany players were due to be tested before they joined the squad on Monday.