Holders City host arch-rivals United in a repeat of last season's semi-final which City won 1-0 before securing their first major trophy for 35 years by beating Stoke City in the final.
January's cup meeting will come almost three months after City stunned their neighbours 6-1 in the league at Old Trafford, signalling their determination to challenge United's years of domination in Manchester.
City have raced into a five-point lead in the Premier League over champions United, who will see the Cup meeting at the Etihad stadium as the perfect chance to exact revenge.
"Great game to kick off this [year's] FA Cup, can't wait," United defender Rio Ferdinand wrote on Twitter.
The match is by far the standout of the draw for the January 7-8 ties, although the jubilant scenes of players from non-league Tamworth celebrating being handed a trip to Premier League Everton were a reminder of the magic of the FA Cup.
There will be plenty of lower league teams hoping to get the better of top-flight opponents, including Championship Leeds United who travel to Arsenal in a repeat of the 1972 final.
Leeds are no strangers to upsets at big stadiums, having stunned Manchester United 1-0 at Old Trafford at the same stage in 2010.
In another match-up between clubs who have contested finals against each other, 2010 winners Chelsea host Championship Portsmouth as the London team's manager Andre Villas-Boas gets his first taste of the famous competition founded in 1871.
Tottenham Hotspur and Aston Villa will come up against League Two sides, with Harry Redknapp's Spurs entertaining Cheltenham Town and Alex McLeish's men heading to Bristol Rovers.
Last year's runners-up Stoke also face fourth-tier opposition in the shape of Gillingham, a familiar club to Potters manager Tony Pulis who played for and managed the Kent outfit.
Manchester is not the only place looking forward to a local derby with Premier League Fulham drawn against League One leaders and fellow Londoners Charlton Athletic and Championship Birmingham City hosting Midlands top-flight rivals Wolverhampton Wanderers.
Apart from the big City v United game, there will be one other all Premier League clash as Newcastle United host struggling Blackburn Rovers.
FA Cup third-round draw:
Middlesbrough v Shrewsbury Town
Nottingham Forest v Leicester City
Manchester City v Manchester United
Dagenham & Redbridge or Walsall v Millwall
Crawley Town v Bristol City
Doncaster Rovers v Notts County
Bristol Rovers v Aston Villa
Tottenham Hotspur v Cheltenham Town
Sheffield Wednesday v West Ham United
Milton Keynes Dons v Queens Park Rangers
Hull City v Ipswich Town
Coventry City v Southampton
Brighton & Hove Albion v Wrexham
Fulham v Charlton Athletic
Birmingham City v Wolverhampton Wanderer
