The Germany winger was a surprise starter for Pep Guardiola's side, with speculation persisting over a possible move to Bayern Munich.
Guardiola admitted before the match there had been a setback in contract negotiations with Sane, as some reports suggest the 23-year-old has already agreed terms with Bayern.
Sane was nonetheless used from the start at Wembley in a front three alongside Raheem Sterling and Bernardo Silva, but was hurt nine minutes in after being fouled by Trent Alexander-Arnold.
He could not continue, having apparently jarred his right knee, and hobbled from the pitch to be replaced by striker Gabriel Jesus.
City took the lead following the free-kick, Sterling scoring from close range against his former club after David Silva flicked the ball into his path.