The fourth-round tie against Mauricio Pochettino's side will now be played on Wednesday, November 6 with a 7:45pm kick-off.
A statement on the club's website read: "Strenuous representations were made to the Football League by Northumbria Police, relating to concerns around public safety in the wider region due to the game's close proximity to the Wear-Tyne derby and Newcastle United's fixture being scheduled on the same evening (October 30).
"The Football League, who oversee fixture scheduling for the competition, has therefore requested that Sunderland's game is moved to the following week."
Sunderland's commercial director Gary Hutchinson said: "We have agreed to move the game with great reluctance, as we know the impact this could have on supporters and appreciate and thank them for their understanding in this matter."
The Football League's chief operating officer, Andy Williamson, added: "It is never ideal for a match to be dated and then moved at relatively short notice.
"Nonetheless, we have listened to the representations made by the police on this matter and have agreed that it is in the wider public interest to re-arrange this match. We apologise for any inconvenience this causes for supporters."