UEFA said United, who finished below champions City in the Premier League last season, would have their fixture reversed.
The quarter-final first-legs will be played on April 9/10 with the return legs scheduled for April 16/17.
"Following a decision made by relevant local authorities, Manchester City and Manchester United cannot play at home on the same night, nor on consecutive nights," UEFA said.
"Should both clubs be drawn within the same sequence (home or away), the team having finished lower in the domestic league the previous season – in this case United - will be reversed in accordance with the UEFA Club Competitions Committee principles.
"In accordance with paragraph 21.01(b) of the UEFA Champions League regulations, the UEFA administration will determine which matches will be played on Tuesday, which matches on Wednesday."
UEFA said that the same rule would apply should both teams advance to the semi-finals.
There is also the possibility that derby rivals United and City could face each other in the quarter-finals or take on fellow Premier League sides Liverpool and Tottenham Hotspur.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Toby Davis)
