Walker picked up the injury in Sunday's 6-3 Premier League home victory over Manchester United and was withdrawn in the first half of the derby. He missed City's 5-0 Champions League victory over FC Copenhagen on Wednesday.
City did not provide a timeframe for Walker's return but the right back, a crucial part of England's set-up under manager Gareth Southgate, is now in a race against time to be fit to start in their World Cup opener against Iran on November 21st.
Walker has 70 caps and was a key member of the teams that reached the Euro 2020 final and 2018 World Cup semi-finals.