Stones, who has been in excellent form for City and England, pulled up while chasing the ball in the 28th minute and gave way to Eliaquim Mangala shortly after.
“He will be out for a long time, four to six weeks I think,” said City manager Pep Guardiola.
With Nicolas Otamendi suspended, club captain Vincent Kompany had slotted in alongside Stones at centre-back for Guardiola’s league leaders.
The injury-prone Kompany, a Belgium international, was making his first league start since August.
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