The Germany international will miss Saturday's Bundesliga clash with FC Augsburg after suffering a thigh injury during the international break. He has since returned to individual training, although no date has been set for his comeback.
Musiala, 23, began the season on the sidelines after two collapses linked to absence seizures during pre-season. Having worked his way back to fitness, the attacking midfielder has suffered another frustrating setback.
Kompany, who experienced numerous injuries during his own playing career, believes Musiala has the strength to overcome the latest challenge.
"I can relate to his story of setbacks. I've experienced that often in my own career. Coming back from that is a great strength," Kompany said on Friday.
The Bayern coach is convinced Musiala will enjoy many more successful years in football.
"I hope he can enjoy playing football again in the coming years, and I believe he will," he added.
"Jamal has always shown that strength. In every situation, he knows how to fight his way back, and he always comes back."
Kompany also highlighted the excitement Musiala brings to the team and supporters when he finds the net.
"We've seen how happy the team and fans are when he scores a goal. We'll experience those moments again," he said.
Robert Andrich has admitted that losing the captaincy at Bayer Leverkusen and falling down the pecking order has been difficult, but the midfielder is determined to fight his way back into the team.
Dani Olmo has no plans to leave Barcelona despite reported renewed interest from Bayern Munich, with the Spain international fully focused on continuing his career at the Catalan club.
Bayern Munich have provided an encouraging update on Jamal Musiala as the Germany international continues his recovery from a muscle injury.
Bayern Munich manager Vincent Kompany believes Michael Olise has already established himself as a world-class player after another outstanding run of form for club and country.
