The striker was forced off midway through the second half as United beat Manchester City, with fears after the game that he had suffered a bad ankle injury.
However, as reported by Sky Sports, scans revealed that Rashford had avoided ligament damage but the bruising sustained will not have subsided before Thursday's game.
Rashford's injury comes as United also prepare to face top-four rivals West Ham on Sunday. The Hammers are six points off United with a game in hand.
Edinson Cavani was absent for the win over table-topping City but could return for the Europa League tie, while Anthony Martial returned in the victory.
Paul Pogba's thigh injury is expected to keep him out. There remains no confirmed date on David de Gea's return following the birth of his daughter.