Arsenal, appearing in the semis for a record 24th time, will meet United at Villa Park, while the other semi will take place at Manchester United's home ground of Old Trafford.
Monday's draw gave Arsenal the hardest possible obstacle in their bid to become the first club since Blackburn Rovers in 1886 to win the FA Cup three years in succession and the first ever to reach four successive finals.
Sunderland were the last team from outside the top division to reach the final when they lost to Liverpool in 1992, while Millwall and Tranmere will replay next week in their bid to reach the last four.
Millwall, who were held to a 0-0 draw at home by Tranmere on Sunday, are looking to reach the semis for the first time since 1937 while Tranmere have never reached the last four.
The final will take place at Cardiff's Millennium Stadium on May 22.
Arsenal and Manchester United are due to meet in a league match at Highbury a week before their Cup tie. It will be the first meeting between the two giants of English soccer since their infamous bust-up at Old Trafford on September 21.
That match ended with six Arsenal players and two United players charged by the FA for the fracas that followed their 0-0 draw.
LATE WINNER
The most famous FA Cup meeting between the clubs, who have won the cup 19 times between them, came in the 1979 final when Arsenal, 2-0 up with two five minutes to play alllowed Manchester United to equalise at 2-2 --
Manchester United's last win over Arsenal in the competition came in a replayed semi-final at Villa Park in 1999 when a Ryan Giggs goal -- recently voted the greatest in the competition's history -- gave United a 2-1 win after United goalkeeper Peter Schmeichel saved a penalty from Dennis Bergkamp.
In all they have met in the Cup 10 times, with Arsenal winning five times, United four and the original semi in 1999 ending in a 0-0 draw. Their last meeting in the competition came last season when Arsenal won 2-0 at Old Trafford in the fifth round.
Sunderland have only met Millwall once in the Cup -- on the last occasion when Millwall reached the semi-finals in 1937.
That match took place at Huddersfield's old Leeds Road ground and Sunderland went on to win the FA Cup for the first time in their history when they beat Preston North End 3-1 in the final.
Sunderland have only met Tranmere -- who have never reached the semis --twice in the competition before -- and had never met them until 1998 when Tranmere won 1-0 at Sunderland in in a fourth round match.
In 2000 they were drawn to face each other again in the fourth round and again at Sunderland, with Tranmere Rovers winning that tie 1-0 as well with a goal from Wayne Allison who is still with the club.
Bookmakers William Hill made Arsenal the 6-5 on favourites to win the Cup following the draw, with Manchester United 6-5 second favourites and Sunderland at 10-1, Millwall 28-1 and Tranmere 50-1.