The Spaniard twisted his ankle in the warm-up ahead of the game with the Danish side.
De Gea limped off the pitch after diving awkwardly in the warmp-up and became the 14th United player to be ruled out of their game against Midtjylland.
De Gea was treated on the pitch after picking up the injury.
Sergio Romero replaced De Gea in the starting line-up.
