The Red Devils will square off against the League Two side at Huish Park on the weekend of January 27-28 having seen off Derby County in the third round.
Tottenham also drew League Two opposition, being matched up with Welsh side Newport County.
Meanwhile league leaders Manchester City will have to travel to face either Cardiff City or Mansfield Town while after defeating Everton in the third round, Liverpool will again be paired up with Premier League opposition as they face West Brom at Anfield.
That will not be the only all-Premier League clash in the fourth round as Southampton will host Watford while Bournemouth could face West Ham should they beat Wigan Athletic and Shrewsbury Town in their respective replays.
|Liverpool vs West Brom|
|Peterborough United vs Fleetwood Town/Leicester City|
|Huddersfield Town vs Birmingham City|
|Notts County vs Wolves/Swansea City|
|Yeovil Town vs Manchester United|
|Carlisle United/Sheffield Wednesday vs Stevenage/Reading|
|Cardiff City/Mansfield Town vs Manchester City|
|MK Dons vs Coventry City|
|Millwall vs Rochdale|
|Southampton vs Watford|
|Middlesbrough vs Brighton|
|Bournemouth/Wigan Athletic vs Shrewsbury Town/West Ham|
|Hull City vs Nottingham Forest|
|Newport County vs Tottenham|
|Norwich City/Chelsea vs Newcastle United|
|Sheffield United vs Preston North End|
Chelsea too face a replay against Norwich City, with a home tie against Newcastle United the reward for the winner.
Nottingham Forest, who stunned Arsenal in the third round, will face off against fellow Championship side Hull City in their fourth-round clash.