Brighton staged a dramatic recovery against Millwall after being 2-0 down with 88 minutes played.
The Seagulls scored twice in the time that remained before winning on penalties to secure a place in the last four.
Brighton boss Chris Hughton said after the draw, "Obviously it;s not the draw we wanted!"
City and Brighton have me just twice before in the FA Cup.
The first occasion was 95 years ago when the Blues triumphed 5-1 on the south coast.
The next meeting was in 1983, with the Seagulls thrashing City 4-0 at the Goldstone Ground on their way to the final.
City beat Brighton 2-0 in the Premier League meeting last September, with Raheem Sterling and Sergio Aguero on the score-sheet.
Semi-final ties will take place at Wembley Stadium on Saturday 6 April and Sunday 7 April.
Ticket details will be announced in due course.