Manager Jose Mourinho will be relieved that it will be a short trip for United this time following their narrow last-16 win over Russian side Rostov.
The first leg will take place in Brussels on April 13, with the second match at Old Trafford a week later.
Anderlecht vs Man Utd
Celta Vigo vs Genk
Ajax vs Schalke
Lyon vs Besiktas
Ties to be played April 13/20.
Mourinho had said of United's last-16 victory: "I think Rostov is a very difficult team to play against because they defend with a block of 10 players.
"It was difficult for everyone. Only Bayern at home scored early and had an easy job, but Atletico Madrid, Anderlecht, Ajax, Sparta Prague, Man United, it was difficult to play against them.
"Our plan was to kill the game when we had energy for that.
"We played in the first half like we were the team that needs to score: we tried to kill in the first half; we hit the post; the goalkeeper saved; we missed chances, so they let the game go open and then when we were dead they were trying.
"My players they fought hard to keep the result and go through."