The fixture will see Reading boss Jaap Stam return to his former club for the first time as a manager.
Notts County or Peterborough will visit Premier League leaders Chelsea.
Arsenal, who hold the record for the most FA Cup wins alongside Manchester United with 12, travel to Championship side Preston.
Liverpool will play the winner of Newport County and Plymouth.
In other ties, non-league Barrow will face League One Rochdale.
The fixtures will be played between January 6 and 9.
Third round draw:
Ipswich v Lincoln City/Oldham
Barrow v Rochdale
Manchester United v Reading
Hull City v Swansea
Sunderland v Burnley
QPR v Blackburn
Millwall v Bournemouth
West Ham v Manchester City
Brighton v MK Dons/Charlton