It means that Hammers will have to pull off a repeat of that famous 1-0 victory at the Theatre of Dreams in January 2001 if we are to continue our dreams of FA Cup glory this season following Saturday's third round victory over Nottingham Forest.
The match at Old Trafford is scheduled for the weekend of January 25/26, but is likely to be rearranged as a live televised game.
The draw was made at the FA's Soho Square headquarters by former FA Cup winning captains Phil Neal and Steve Perryman at 1pm on Monday - a return to the competition's traditional draw time of years gone by.
There were two other all-Premiership ties drawn out of the hat - Blackburn Rovers will host Bolton Wanderers or Sunderland, and Fulham play Charlton Athletic in a London derby.
Holders Arsenal were drawn away to non-league Farnborough Town, while our Conference neighbours Dagenham & Redbridge face a trip to Norwich City or Brighton if they can overcome Plymouth Argyle in their third round replay at Victoria Road next week.