The Foxes, who are the one remaining non-Premier League side in the competition, will host Manuel Pellegrini's charges at the King Power Stadium in the week commencing 16 December.
Elsewhere, Mark Hughes faces a reunion with his former side after Stoke City were drawn at home to Manchester United.
Tottenham, who like Stoke required penalties to reach the last eight, are at home to London rivals West Ham United. The Hammers were 3-0 winners when they visited White Hart Lane earlier this month in the Premier League.
Sunderland's victory over Southampton has earned them a plum home draw against Chelsea.
Capital One Cup quarter-final draw
Leicester v Manchester City
Stoke v Manchester United
Sunderland v Chelsea
Tottenham v West Ham
Ties to be played week commencing 16 December