The Argentine was stretchered off within 15 minutes of the Premier League holders' season opener against Southampton on Sunday and has been undergoing scans to assess the extent of the damage.
However, the return to action to his compatriot, Carlos Tevez, who scored the opener in Sunday's 3-2 victory, after being absent for eight months last year gives the Belgian hope.
Kompany told reporters after the match: "We lost Sergio, which was sort of a blow, but I just go back to when we lost Carlos for most of [last] season and coped well with that.
"I hope Sergio won't be out for that long but I would point to last season where we had to cope with these kind of issues and we did it very well. If we have to, I'm sure we will again.
"I don't want to speculate too much about Sergio because I don't know if he is going to be out for any length of time, but having Carlos at his best level is obviously a big bonus for us. He is one of the best strikers in the world.
|IN THE SWING OF THINGS
|15/2||Carlos Tevez is a joint-favourite 15/2 to be the Premier League's top scorer with bet365|
"People talk about new signings, but to have Carlos back to his best means we are better than we were last season, so we have strengthened.
"I never thought we would lose," the defender continued of the match itself. "I can't explain why but, when we were 2-1 down, I still knew we would go on and win the game, and it turned out that way.
"I'm very happy to see we have that strength of character and belief in our team. We made a tactical mistake but it won't happen again. We have to respect Southampton's performance and overall we are happy to get away with a victory."
New signing Jack Rodwell, secured in a deal that could reach £17 million from Everton, made his debut against Saints but endured an unfortunate start when his giving-away of possession led to Steven Davis' goal that put the visitors 2-1 in front.
Kompany, however, insisted: "Jack has settled in very well. I'm sure he'll be an asset to our team and I think this game was the right time to bring him in with Liverpool coming up next week."