Sane, who cost £37m plus add-ons when he joined City from Schalke in August 2016, has yet to start a Premier League game for the champions this season.
Sane was controversially omitted from Germany's World Cup squad that travelled to Russian Federation this summer, where the 2014 champions crashed out at the group stage.
The decision comes after Germany's 0-0 draw in the UEFA Nations League against France, in which Sane made a seven-minute cameo.
The 22-year-old winger has endured a hard few months since being nominated for various individual Premier League awards at the end of last season.
But he will miss the friendly against Peru on Sunday with permission from the coach.
Global team-mate Toni Kroos claimed earlier this week that 22-year-old Sane, who has made 13 senior appearances for Germany, was not fulfilling his potential and must improve his attitude.
Now, Sane will return to Manchester and re-join his club, who he also did not play for after Pep Guardiola left him out of the side's last Premier League game, a 2-1 win over Newcastle United.
"You sometimes get the feeling that it doesn't matter to him if we win or lose", the Real Madrid player said prior to playing Les Blues on Thursday, September 6.