The fixture is a repeat of the 1956 FA Cup Final and the first meeting between the two sides since 2011.
The tie also mirrors the FA Youth Cup third round draw which was made earlier this month.
Blues last faced Manchester City in an FA Cup tie exactly two decades ago when goals from Martin Grainger and Dele Adebola were unable to prevent a 3-2 defeat.
Chris Hughton took charge of the last Blues side to face Manchester City with Owen Hargreaves and Mario Balotelli scoring in a 2-0 Carling Cup defeat at the Etihad.
In fact, Aitor Karanka’s men will not only be aiming to achieve an FA Cup upset but also become the first Blues side to beat Man City in the last 13 visits.
You have to go back to April 1998 to find Blues’ last victory over City away from St. Andrew's. Dele Adebola's last-gasp effort enough to seal a double over the Citizens in an old Division One clash.
More recently, the Club reached the fifth round of the competition last season, edging out Blackburn Rovers and Coventry City before suffering a narrow defeat to Premier League side Leicester City.
Blues are yet to lift the prestigious trophy but have reached the final on two occasions, in 1931 and in the aforementioned 1956 final, eventually losing to West Bromwich Albion and Manchester City respectively.
The draw was broadcast live on BBC One on Monday evening and was conducted by former Blues midfielder Robbie Savage.
All 32 third round ties will take place across the weekend of Saturday 9 and Sunday 10 January 2021.
A date for Blues' match against Manchester City will be confirmed in due course.