The England international pulled up half an hour into the Citizens' 2-0 win over Leicester City on Saturday afternoon with a hamstring complaint.
Kompany, who returned to the starting lineup in the same match after more than two months on the sidelines, hopes that his own injury struggles can act as an inspiration to Stones as he begins his road to recovery.
"Stonesy was one of the outstanding performers so far," he told reporters. "If there's one thing I can give him it's that it's something you have to go through in your career at times and there's no reason why you shouldn't come out stronger for it.
"Hopefully it's not too bad and when he comes back we'll need him as much as we'll need anyone otherwise we won't achieve all these targets we have."