Musiala came off second best in an ugly collision with PSG goalkeeper Gigio Donnarumma during Bayern's Club World Cup quarterfinal defeat on Saturday.
In the aftermath, Kompany stated: "After what happened to Musiala, the emotion was intense, because nobody liked to see that.
"We hope it's not too serious and that he receives the best medical care. These things happen. We have to stay calm. It was an accident, one minute before the end of the first half... We were unlucky.
"It was very difficult. I've never been so angry, and it wasn't directed at the players, but because it happened to him. There are many important things in life, but for these young people, football is their life. You feel helpless. What really gets me going is not the result, but what happened to Jamal. It's not looking good. If you look at the pictures, you can see he's injured.
"But I won't make a diagnosis."
Match could've gone our way
On the 2-0 defeat, Kompany added, "We weren't rewarded for our game, not because of our football, but because that's how it is. They also made mistakes.
"The only thing that saddens me is that we didn't capitalize on our last two chances. The match was a close one. We could have led, even 2-0."
It's since emerged Musiala is facing 4-5 months sidelined after suffering a fracture of the left fibula and damaged ligaments.