The Belgium defender suffered a thigh injury in City's defeat of Everton a fortnight ago.
Recent reports had suggested the 27-year-old could be back in contention for the trip to Upton Park on Saturday but, while he has made good progress, he will not be considered.
Manager Manuel Pellegrini said: "Vincent is working hard. He is not ready to play but I hope next week he will be."
With a tough week ahead, Pellegrini does not want to take any chances with his influential skipper.
City travel to CSKA Moscow in the Champions League on Wednesday and then face Chelsea at Stamford Bridge the following Sunday.
Kompany has already missed three games this season after sustaining a groin injury in the opening match against Newcastle.
He was sorely missed during that absence, as he was when injured at a critical stage of last season.
Martin Demichelis, who has not featured since his arrival in August due to a knee injury, is not yet fit to come in but could be in contention in the coming days.
Pellegrini said: "Demichelis played last Wednesday, 45 minutes for the under-21s.
"I think he is in the same shape as Kompany. I hope that next week both of them could be fit."
City head to West Ham looking for their first away win of the season after defeats at Cardiff and Aston Villa and a draw at Stoke.
Pellegrini said: "I think we deserve more points playing away the way we are playing, but the reality says we have one point from nine so we need to win."
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- Manuel Pellegrini