The Bayern Munich pair were called up to Hansi Flick's 24-man squad for two UEFA Nations League fixtures against Hungary and Italy this month.
Both Neuer and Goretzka, who have 147 international caps between them, are now self-isolating away from the rest of the first-team squad and will depart from the team hotel.
A statement from German FA read: "Leon Goretzka (27) and Manuel Neuer (36) tested positive for the Coronavirus on Wednesday morning.
"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 have also confirmed that Hoffenheim goalkeeper Oliver Baumann has been called up as a replacement for Neuer, while any further squad announcements will be made later in the day.
Earlier this week, Borussia Dortmund attacker Marco Reus was forced to withdraw from the national team squad after being stretchered off with an ankle injury in the Bundesliga win over Schalke 04 last weekend.
The 33-year-old, who has been hampered with injuries throughout his career, missed Germany's triumphant 2014 World Cup campaign due to injury and there were initially fears that he could miss the trip to Qatar.
However, Reus is only set to miss the next three to four weeks with ankle ligament damage and he could return to action in the middle of October.
Germany sit second in League A Group 3 of the Nations League after four matches, and they are now preparing for their penultimate group game at home against leaders Hungary on Friday, before facing England at Wembley Stadium in their final fixture three days later.