The quarter-finals – and each game after – will be played in Germany and over just 90 minutes rather than two legs.
United easily saw off LASK in the last round, while Copenhagen were impressive in beating Turkish SuperLig champions Istanbul Basaksehir.
The Danes have never been this far in the competition before, while United won it back in 2017.
Here’s all you need to know about the game.
When is it and what time is kick-off?
The match will begin at 8pm BST on Monday 10 August at Stadion Koln, in Germany.
How can I watch it online and on TV?
The game will be broadcast live on BT Sport 1 and BT Sport Extra 1, as well as BT Sport Ultimate.
Subscribers can also stream the match on the BT Sport website and app.
United: Romero; Wan-Bissaka, Bailly, Maguire, Williams; Fred, Pogba; Greenwood, Fernandes, Rashford; Martial.
Copenhagen: Johnsson; Varela, Nelsson, Bjelland, Boilesen; Zeca, Stage; Biel, Wind, Falk; Daramy.
Man United — 2/7
Draw — 67/13
Copenhagen — 12/1