The club used frost covers to protect the pitch on Tuesday night, but with the temperature expected to remain below zero there were concerns the ground would freeze during the game.
Referee Keith Stroud made the decision after an inspection, so Accrington Stanley’s players and supporters would not travel.
U’s boss Chris Wilder felt there was no choice other than to postpone the tie until next Tuesday.
He said: “Not really, it’s a difficult decision for a referee when they have to say what the conditions are going to be like after 10pm – because there was the potential that game could have gone to extra time.”
The delay may, however, benefit United, who had fitness doubts over several players.