City defeated United 1-0 in the FA Cup semi-finals at Wembley en route to winning the competition last season and they will host Sir Alex Ferguson's side at Eastlands over the weekend of January 7/8.
Roberto Mancini's side, who beat Stoke in the final to claim their first trophy in 35 years, are currently five points clear of reigning champions United in the Premier League as they seek to snatch the English title away from Old Trafford.
The match has added spice as it will be the first Manchester derby since City's astonishing 6-1 league triumph at Old Trafford in October.
The tie was one of only two all-Premier League encounters in the third round draw, with Newcastle hosting Blackburn in the other.
Chelsea take on Portsmouth at Stamford Bridge in a rematch of the 2010 FA Cup final which the west London club won 1-0 to complete their first ever league and cup double.
Arsenal will host Championship side Leeds and Liverpool are at home to either Southend or Oldham.
Tottenham take on League Two club Cheltenham and Everton host National Conference outfit Tamworth.
Draw for the English FA Cup third round made at Wembley on Sunday:
Middlesbrough v Shrewsbury
Nottingham Forest v Leicester
Manchester City v Manchester United
Dagenham and Redbridge/Walsall v Millwall
Crawley v Bristol City
Doncaster v Sutton United/Notts County
Bristol Rovers v Aston Villa
Tottenham v Cheltenham
Sheffield Wednesday v West Ham
Milton Keynes Dons v QPR
Hull v Ipswich
Coventry v Southampton
Brighton v Wrexham
Fulham v Charlton
Birmingham v Wolves
Norwich v Burnley
Arsenal v Leeds
Derby v Crystal Palace
Fleetwood/Yeovil v Blackpool
Swindon v Wigan
Barnsley v Swansea
Chelmsford/Macclesfield v Bolton
Newcastle v Blackburn
Everton v Tamworth
Sheffield United v Salisbury/Grimsby
Liverpool v Southend/Oldham
Gillingham v Stoke
Chelsea v Portsmouth
Watford v Bradford
Peterborough v Sunderland
West Brom v Cardiff
Reading v Stevenage
Ties to be played on the weekend of January 7/8
Source: AFP
Source: AFP