Later this week, the Gunners and Red Devils will meet in an exact replica of the tie that will take place at the Emirates Stadium between January 9 and January 13.
Monday's draw has ensured that United will be making two visits to North London to meet Mikel Arteta's side as they bid to defend the trophy that they lifted in May.
Meanwhile, National League outfit Tamworth have been provided with a blockbuster tie of their own in the form of Tottenham Hotspur.
Manchester City will go up against Salford City, partly-owned by several Manchester United legends, while Premier League leaders Liverpool will welcome Accrington Stanley to Anfield.
Morecambe will make the trip to Stamford Bridge to face Chelsea, and Harrogate Town have been handed a Yorkshire derby at Leeds United.
Newcastle United play host to another League Two side in the form of Bromley, with the second and final all-Premier League tie being Aston Villa's clash with West Ham United.
FA Cup third-round draw in full
Southampton vs. Swansea City
Arsenal vs. Manchester United
Exeter City vs. Oxford United
Leyton Orient vs. Derby County
Reading vs. Burnley
Aston Villa vs. West Ham United
Norwich City vs. Brighton & Hove Albion
Manchester City vs. Salford City
Millwall vs. Dagenham & Redbridge
Liverpool vs. Accrington Stanley
Bristol City vs. Wolverhampton Wanderers
Preston North End vs. Charlton Athletic
Chelsea vs. Morecambe
Middlesbrough vs. Blackburn Rovers
Bournemouth vs. West Bromwich Albion
Mansfield Town vs. Wigan Athletic
Tamworth vs. Tottenham Hotspur
Hull City vs. Doncaster Rovers
Sunderland vs. Stoke City
Leicester City vs. Queens Park Rangers
Brentford vs. Plymouth Argyle
Coventry City vs. Sheffield Wednesday
Newcastle United vs. Bromley
Everton vs. Peterborough United
Wycombe Wanderers vs. Portsmouth
Birmingham City vs. Lincoln City
Leeds United vs. Harrogate Town
Nottingham Forest vs. Luton Town
Sheffield United vs. Cardiff City
Ipswich Town vs. Bristol Rovers
Fulham vs. Watford
Crystal Palace vs. Stockport County
FC Oleksandriya 
Dynamo Kyiv 
VFL Wolfsburg 
1899 Hoffenheim 
Ajax 
Utrecht 
Everton 
Wolverhampton 
Manchester City 
Nottingham Forest 
Newcastle 
Liverpool 
Southampton 
Chelsea 
RB Leipzig 
Eintracht Frankfurt 
Rangers 
Kilmarnock 
Fiorentina 
Empoli 
Aberdeen 
Celtic 
Athletic Bilbao 
Real Madrid 
Ejea 
Valencia 
Arsenal 
Manchester Utd 
Shakhtar Donetsk 
Vorskla Poltava 
Cacereno 
Atletico Madrid 
Lazio 
Napoli 
Ue Olot 
Sevilla 
Bournemouth 
Tottenham 
Inter 
Parma 
Valenciennes 
Bordeaux 
PSV 
Twente 
Atalanta 
AC Milan 
Auxerre 
Paris Saint Germain 
Spartak Moscow 
Nizhny Novgorod 
Bayer Leverkusen 
FC ST. Pauli 
Bayern Munich 
FC Heidenheim 
FC Augsburg 
VFL Bochum 
Werder Bremen