Musiala picked up a hamstring problem playing for Bayern Munich against Bayer Leverkusen in the Bundesliga on Sunday.
The 20-year-old was only fit enough to start from the bench and replaced Thomas Muller at half time as Bayern Munich lost 2-1.
Musiala has enjoyed an impressive season for the Bavarians thus far, having scored 15 goals and provided 11 assists in 35 appearances across all competitions.
As host nation Germany are not required to partake in the qualifiers for EURO 2024 and will be fulfilling friendly matches against Belgium and Peru during the international break.
Speaking to reporters ahead of the international break, Germany manager Hansi Flick said: "We [had] all hoped that Jamal would be fit, because he has unique qualities."
"That's why it's a shame for everyone that he won't be with us.
"We hope he is fit again as soon as possible and that he is back playing after the international matches."
Germany have opted not to call up a replacement for Musiala.
Musiala has won 20 caps for Germany and played at the last two international tournaments since making his debut in 2021.
