League Two Yeovil Town, the lowest-ranked side left in the FA Cup, will host 12-time winners Manchester United in the fourth round.
Tottenham will also go to League Two opposition as they play Newport County.
Premier League leaders Manchester City have been drawn away to Cardiff City or Mansfield, while Nottingham Forest, who knocked out holders Arsenal on Sunday, are at Championship rivals Hull.
The fourth-round ties will be played on the weekend of 26-29 January.
- Watch all of the latest FA Cup highlights and reaction here
- I spoke to Sir Alex about drawing Man Utd in the FA Cup – Yeovil manager Darren Way
Premier League champions Chelsea have the prospect of a home tie against Newcastle if they overcome Championship side Norwich in a replay that will be shown live on BBC One on 17 January.
Seven-time winners Liverpool were the first team drawn and will welcome top-flight rivals West Brom to Anfield.
It is the second time in three years that Manchester United, second in the Premier League, have faced Yeovil Town in the competition.
The two last met in January 2015 when United won 2-0 in the third round under previous manager Louis van Gaal.
‘What dreams are made of’
Yeovil beat League One side Bradford to reach round four and their manager Darren Way is looking forward to welcoming Manchester United and their manager Jose Mourinho to Huish Park.
“The attention is going to draw to the town, which has a population of about 40,000. The club needs it at this time,” Way told BBC Radio 5 live.
“To see Jose Mourinho come down and hopefully Sir Alex [Ferguson] – because I know he follows the club – it’s a great moment for everyone involved with the club.
“We sit at home and read books about Mourinho and Guardiola, but to speak to them face-to-face there isn’t a price to put on that. To share that moment in my office hopefully before and after the game is what dreams are made of.”
‘I’m buzzing to face Spurs’
Newport produced an FA Cup shock in the third round by beating Championship side Leeds United and boss Mike Flynn says drawing Tottenham is just reward for his players’ efforts.
“I’m absolutely buzzing about the draw,” he said.
“It’s huge for the club and the players deserve it for their hard work. We can’t wait.”
Fourth-round draw in full:
Liverpool v West Brom
Peterborough v Fleetwood/Leicester
Huddersfield v Birmingham
Notts County v Wolves/Swansea
Yeovil v Manchester United
Carlisle/Sheffield Wednesday v Stevenage/Reading
Cardiff/Mansfield v Manchester City
MK Dons v Coventry
Millwall v Rochdale
Southampton v Watford
Middlesbrough v Brighton/Crystal Palace
Bournemouth/Wigan v Shrewsbury/West Ham
Hull v Nottingham Forest
Newport County v Tottenham
Norwich/Chelsea v Newcastle
Sheffield United v Preston