Manchester City will play Chelsea, while Arsenal are at home to Liverpool in the FA Cup fifth round.
Everton boss Roberto Martinez will face one of his former clubs, Swansea, while Sunderland will host Southampton in the the other all-Premier League tie.
Premier League strugglers Cardiff are at home to holders Wigan, Hull travel to Brighton and Sheffield Wednesday host fellow Championship side Charlton.
The games will be played on the weekend of 15-16 February.
The round's other tie sees Sheffield United or Fulham host Nottingham Forest or Preston - the only two ties that need fourth-round replays.
The two stand-out ties bring together the Premier League's current top four.
It means leaders Arsenal are now scheduled to play Liverpool and Manchester United in the league, the Reds again in the FA Cup and Bayern Munich in the Champions League in the space of 12 days.
Second-placed Manchester City's game with Chelsea, who are third, will take place either within four days of hosting Barcelona in the Champions League.
Of the trip to the Etihad, Chelsea boss Jose Mourinho told ITV: "No problem. If you want to be the best, you have to play against the best, so it's good for us. One team is the end product. One team needs to improve and has a long way to go. Good experience, good game, big game."
There are only two fixtures guaranteed to be between Premier League and Football League sides, with Brighton hosting Hull and defending champions Wigan visiting Ole Gunnar Solskjaer's Cardiff.
Sheffield Wednesday play Charlton Athletic with one of the Championship relegation rivals guaranteed a quarter-final spot.
Full fifth round draw
Manchester City v Chelsea
Sheffield United or Fulham v Nottingham Forest or Preston North End
Arsenal v Liverpool
Brighton & Hove Albion v Hull City
Cardiff City v Wigan Athletic
Sheffield Wednesday v Charlton Athletic
Sunderland v Southampton
Everton v Swansea City
Check out the full FA Cup fifth round draw and have your say on the BBC Sport Facebook page.