The captain faced a late push to be ready after suffering a calf problem while on international duty with Belgium.
Pep Guardiola said: “I think he will not be able [to play] tomorrow. It will be short term, but I think for the next time he will not be able to play.”
Kompany completed 90 minutes for his national team in their 9-0 win over Gibraltar in August, despite taking a knock.
He then missed Belgium’s 2-1 win over Greece on Sunday.
Guardiola added: “I am sad. I would like him to be fit.
“He made a huge effort, our physios and people worked a lot to take care of him, so the last seven, eight or nine games of last season he played without problems for 90 minutes.
“This pre-season, we’ve taken care of him and he played these three games for 90 minutes with no problem at all.
“Now it’s the start of the part where we play every three days, up to now it was just one game a week, and unfortunately we lost him. Again, we’ll try to recover as soon as possible.”
City were interested in signing a new central defender in the summer, but failed to bring one in - with West Brom digging their heels in on their £30m valuation of Jonny Evans.
The two clubs didn’t get close to agreeing a fee, with City bidding £18m.
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Guardiola could be left ruing the decision not to meet their asking price, admitting a new centre-back was always on the radar.
He said: “The window is over. So with Vincent or without Vincent we thought maybe we needed another one.
“But we have [Eliaquim] Mangala, we have Tosin [Adarabioyo], and we have other options with other players who can play in that position."
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