The two Premier League giants will face off again at Stamford Bridge on April 1 after the Blues fought back from 2-0 down in the original tie to force a rematch.
The Blues fought back from two goals down in the original fixture at Old Trafford on March 10.
The hosts had led through goals from Chicharito and Wayne Rooney after just 11 minutes, but second half strikes from Eden Hazard and Ramires forced the draw, and a replay at Stamford Bridge.
The two sides have played out three high-scoring fixtures this season across all three domestic competitions, with the Red Devils triumphing 3-2 at Stamford Bridge in the league, before losing 5-4 after extra time in the Capital One Cup fourth round.
The rearranged fixture also sees Chelsea's Premier League clash at Southampton move to Saturday 30 March.