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.
