Bristol City's trip to Premier League leaders Manchester City will kick off the Carabao Cup semi-finals.
Lee Johnson's side, bidding to do the Manchester double after their stunning upset of holders United on Wednesday, will travel to the Etihad Stadium on January 9.
The Robins are looking for their fifth consecutive Premier League scalp having previously knocked out Watford, Stoke and Crystal Palace.
Chelsea will host Arsenal the following night on January 10 in the first leg of their semi-final.
The reverse fixtures take place a fortnight later, with Bristol City hosting Pep Guardiola's side on January 23 and Chelsea travelling to the Emirates Stadium on January 24.
Both legs of the clash between Arsenal and Chelsea, as well as the final, will see video assistant referees used for the first time in a Football League competition.