United, who beat Real Sociedad 4-0 on aggregate in the previous round, will face the seven-time European champions in a two-legged encounter after they squeezed past Red Star Belgrade on away goals.
The tie will pit Zlatan Ibrahimovic against his former club in United, where he won the 2017 edition of the Europa League.
The Swede has been in fine form this season as Milan bid for a first Italian league title since 2011, scoring 14 Serie A goals in 13 appearances at the age of 39.
United will be considered favourites for the tie however as they sit second in the Premier League having lost just once in the English top flight since the start of November.