Pep Guardiola's side could secure an unprecedented quadruple this season but they will need to overcome a Chelsea side who remain unbeaten in all competitions since Thomas Tuchel took charge in January.
City, who lead the Premier League by 14 points and have already booked a Wembley date this season after reaching the League Cup final on April 25, edged past Everton on Saturday with a 2-0 win.
Leicester will have the chance to reach their first FA Cup final since 1969 and win the competition for the first time in their history.
Both games will be played at Wembley on the weekend of April 17 and 18.
Draw in full:
Leicester vs. Southampton
Chelsea vs. Manchester City