The Dutchman was injured on international duty with his nation against Spain in Amsterdam.
He came off after six minutes clutching his hamstring, which could indicate a long layoff.
While Ake is not first choice at City when everyone is fit, his versatility is key to their squad depth.
Losing him for several weeks would be a big blow for manager Pep Guardiola as he aims to challenge for the Premier League and Champions League trophies.
Ake arrived at City in the summer from Bournemouth.