The teams, who were among the favourites to win the competition and are likely to challenge each other in the race for the title, will meet at Emirates Stadium over the weekend of January 6 and 7.
Teams from the Premier League and second-tier Championship enter the FA Cup at the third round stage.
Holder Manchester City was drawn to play Division Two's Huddersfield Town at the Etihad Stadium. Last season's beaten finalist Manchester United travels to Division Three's Wigan Athletic, which caused one of the biggest upsets in recent history when beating City in the final to win the trophy in 2013.
Division Two's Sunderland hosts Newcastle United in a northeast derby.
All-Premier League ties include Tottenham vs Burnley, Crystal Palace vs Everton and Brentford vs Wolverhampton Wanderers.