City, defending Carabao Cup champions will take on League 1 promotion-chasers Oxford United away.
The Blues played the U's last season at the Third Round stage, winning 3-0 at the Kassam Stadium.
Gabriel Jesus, Riyad Mahrez were all on target against Karl Robinson's side.
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Elsewhere, Manchester United drew the competition's lowest-ranked side Colchester United, while Leicester City host Everton and Villa host Liverpool.
Carabao Cup: Quarter-final draw
Oxford United v City
Manchester United v Colchester
Everton v Leicester City
Aston Villa v Liverpool
City are unbeaten in the competition since 2016 and will be keen to try and win the cup for a third successive season.