City and Bury were drawn at home to Hull in Monday evening's fourth round draw live on The One Show on BBC ONE.
After a goalless draw between the two sides at Gigg Lane on Saturday, City and Bury will play each other again in the replay on Tuesday 19 January 2016 at the Coral Windows Stadium for the right to host Steve Bruce's Tigers.
Fourth round ties are scheduled to be played over the weekend of 30/31 January.
Hull booked their place in the fourth round with a 1-0 win over Brighton & Hove Albion.