Musiala has been one of Bayern's standout players this season with 15 goals and 12 assists in all competitions. He is their top scorer in the Bundesliga with 11 goals.
"We all hoped that Jamal would be fit, because he has unique qualities," Flick said.
"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."
Bayern will be concerned with the club set to play league leaders Borussia Dortmund in a potential title-deciding clash on their return from the international break on April 1. Dortmund have a one-point lead over Bayern after 25 games.
Bayern also play Freiburg in the DFB Pokal quarter-finals while they face Manchester City in the Champions League quarter-finals later next month.
Musiala is the second German player to be ruled out after defender Armel Bella Kotchap also withdrew due to a shoulder injury. AC Milan defender Malick Thiaw was called up in his place but Flick chose not to replace Musiala.
