The game at Elland Road will be played on Sunday, March 8, with a 4.30pm kick-off time and will be shown live on TNT Sports 1 and discovery+.
Ticket details have yet to be confirmed.
New dates will have yet to arranged for the Canaries Championship fixtures away at Southampton - which was due to have been played on Saturday, March 7 - and at home to Sheffield United, which was scheduled for Tuesday, March 10.
Norwich reached the fifth round of the FA Cup after beating West Bromwich Albion 3-1 on Saturday, having beaten Walsall 5-0 in the third round.
Leeds teed up the reunion with their former Canaries boss Daniel Farke by beating Birmingham City - this weekend's visitors to Carrow Road - in a penalty shootout.