Liverpool will face Everton in the FA Cup third round, while holders Arsenal will travel to Nottingham Forest.
Premier League leaders Manchester City have a home tie against Burnley, Manchester United host Derby and Chelsea are away at Norwich.
Slough Town, the lowest-ranked side in the draw, will travel to Doncaster if they beat Rochdale on Monday.
Fellow seventh-tier side Hereford will face Leicester if they overcome Fleetwood in a replay.
Four non-league sides were involved in the draw, though none are guaranteed a place in the third round.
National League side AFC Fylde will head to Premier League Bournemouth if they see off Wigan in a replay. Woking, who also play in the fifth tier, know victory over Peterborough in their replay will earn them a trip to Championship side Aston Villa.
In the pick of the other ties, AFC Wimbledon will travel to Wembley to take on Tottenham, Middlesbrough face Sunderland and Brighton & Hove Albion will host Crystal Palace – the latter one of only three all-Premier League contests.
Ties will take place on the weekend of 6-7 January 2018.
The third-round draw in full:
Ipswich Town v Sheffield United
Watford v Bristol City
Birmingham City v Burton Albion
Liverpool v Everton
Brighton & Hove Albion v Crystal Palace
Aston Villa v Woking or Peterborough United
Bournemouth v AFC Fylde or Wigan
Coventry City v Stoke City
Newport County v Leeds United
Bolton Wanderers v Huddersfield Town
Port Vale v Bradford City
Nottingham Forest v Arsenal
Brentford v Notts County
Queens Park Rangers v MK Dons
Manchester United v Derby County
Forest Green Rovers or Exeter City v West Bromwich Albion
Doncaster Rovers v Slough Town or Rochdale
Tottenham Hotspur v AFC Wimbledon
Middlesbrough v Sunderland
Fleetwood or Hereford v Leicester City
Blackburn Rovers or Crewe Alexandra v Hull City
Cardiff City v Mansfield Town
Manchester City v Burnley
Shrewsbury Town v West Ham United
Wolverhampton Wanderers v Swansea City
Stevenage v Reading
Newcastle United v Luton Town
Millwall v Barnsley
Fulham v Southampton
Wycombe Wanderers v Preston North End
Norwich City v Chelsea
Gillingham or Carlisle United v Sheffield Wednesday