The Bayern Munich goalkeeper has picked up a calf problem and will not be involved in the friendly against Gareth Southgate's side or the World Cup qualifier in Baku, the German Football Association (DFB) confirmed.
"The 30-year-old will now be treated at his club, Bayern Munich," the DFB said.
Paris Saint-Germain goalkeeper Kevin Trapp has been called up by Joachim Low to replace Neuer.
The 26-year-old, who has made 22 appearances for Unai Emery's side this season, is yet to win a senior cap for his country.
Germany hosts England on Thursday before facing Azerbaijan four days later.