Premier League champions Manchester City are at home to Burnley, while Tottenham face a tough trip to Crystal Palace.
Holders Chelsea have an easier task with Sheffield Wednesday or Luton to travel to Stamford Bridge.
Wolves’ reward for beating Liverpool 2-1 on Monday is a trip to either Shrewsbury or Stoke.
The ties will be played between January 25th and 28th.
Draw in full:
Swansea v Gillingham
AFC Wimbledon v West Ham
Shrewsbury or Stoke v Wolves
Millwall v Everton
Brighton v West Brom
Bristol City v Bolton
Accrington v Derby or Southampton
Doncaster v Oldham
Chelsea v Sheffield Wednesday or Luton
Newcastle or Blackburn v Watford
Middlesbrough v Newport
Manchester City v Burnley
Barnet v Brentford
Portsmouth v QPR
Arsenal v Manchester United
Crystal Palace v Tottenham