City and Swansea City have never met before in the FA Cup.
The first and only meeting in cup competitions came in 2016, with the Blues winning 2-1 at The Liberty Stadium on the way to winning the Capital One Cup.
City are unbeaten in 12 meetings with the Swans, who lost their Premier League status last season.
The Blues have won 10 and drawn two of those dozen clashes and have won 24 of the 35 meetings overall.
City beat Swansea 4-0 away last season, and 5-0 at home.
They currently sit in 13th position in the Championship table - Bersant Celina will have the chance of facing the Blues for the first time since leaving the Club last year.
FA Cup 6th round - full draw:
Swansea City v Manchester City
Watford v Crystal Palace
Wolves v Manchester United
Millwall v Brighton
The quarter finals are scheduled to take place between Friday 15 March and Monday 18 March - ticket details will be released in due course.