The defender, signed from Bournemouth in the summer, left the field holding his left hamstring.
He has made six appearances since joining the Club, operating at both left-back and centre-half.
City's next match is away at Tottenham on Saturday 21 November.
After the game, Ake posted a tweet on his personal Twitter account, expressing his frustration but adding he hoped to be 'back soon.'
Stay tuned to ManCity.com for updates on Ake's condition.
Sergio Canales opened the scoring for Spain in the Amsterdam ArenA, but Donny van de Beek's equaliser early in the second half saw the game end in a draw.
Frustrating night! Hope to be back soon🙏🏾 pic.twitter.com/a2EPosFVnA— Nathan Aké (@NathanAke) November 11, 2020
Gundogan, Zinchenko and Silva in action