United knocked out Spurs 2-1 at Elland Road in the fourth round to book a trip to the Etihad Stadium in the pick of the fifth round ties.
Non-league Luton, who claimed a famous 1-0 win at Norwich yesterday, missed out on a plum draw with a top Premier League side as they got Millwall at home.
FA Cup fifth-round draw:
Huddersfield/Leicester v Wigan
MK Dons v Barnsley
Oldham v Everton
Luton v Millwall
Arsenal v Blackburn
Man City v Leeds
Man Utd v Reading
Middlesbrough v Brentford/Chelsea
* Ties to be played on the weekend of February 16 and 17.