They stretched their unbeaten run to nine matches with a 5-1 win at Championship (second-tier) side Milton Keynes Dons in the FA Cup fourth round on Sunday.
City, who are bidding for the title as well as seeking success in the Champions League and League Cup, where they face Liverpool in the final, also enjoyed an easy away win with a 4-0 success at Aston Villa on Saturday.
Holders Arsenal, bidding to become the first team since 1886 to win the FA Cup for three years in a row, will meet Championship side Hull City in the competition for the third year running.
Arsenal beat Hull 3-2 after extra time in the 2014 final, having trailed 2-0 after eight minutes, and retained the Cup last season after starting their defence of the trophy with a 3-0 win over Hull in the third round at the Emirates.
The last club to win the FA Cup for three years running, and the last team to defeat Arsenal in the competition in 2013, were Blackburn Rovers, whose reward for beating Oxford United 3-0 on Saturday is a home tie against Liverpool or West Ham United.
The second-tier side will play the winners of next week's replay after the pair drew 0-0 at Anfield on Saturday.
Shrewsbury Town, battling against relegation from League One, scored two late goals to beat Sheffield Wednesday 3-2 on Saturday and are rewarded with a glamorous home tie against Manchester United, whose 11th and last triumph came in 2004.
It is Shrewsbury's first appearance in the fifth round since 1991 which was also the year eight-times winners Tottenham Hotspur last lifted the trophy.
Spurs will be hoping to take another step towards ending that long wait when they face Crystal Palace in a London derby at White Hart Lane.
Twelve top flight teams are left in the competition and, as well as the Chelsea v Manchester City and Spurs-Palace ties, Bournemouth will take on Everton, 3-0 winners at Carlisle United on Sunday, in the other all-Premier League clash.
The draw:
Chelsea v Manchester City; Reading (II) v West Bromwich Albion or Peterborough (III); Watford v Leeds United (II); Shrewsbury Town (III) v Manchester United; Blackburn Rovers (II) v Liverpool or West Ham United; Tottenham Hotspur v Crystal Palace; Arsenal v Hull City (II), Bournemouth v Everton.
Ties will be played between Feb. 19-21
(Reporting by Mike Collett; Editing by Ken Ferris)
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