Ole Gunnar Solskjaer confirmed that neither summer signing would be travelling with the rest of the squad to Turin for Thursday’s last-32 first leg tie.
Cavani and Van de Beek both finished Sunday’s 1-1 draw with West Bromwich Albion at the Hawthorns, with the latter introduced as a second-half substitute.
Solskjaer did not reveal the severity of the injuries but confirmed that neither would be available for the trip to play Sociedad.
“Donny and Edinson are injured unfortunately, muscle injuries, so they won’t travel,” he said.
Anthony Martial and Scott McTominay will make the trip but face late fitness tests to determine their involvement at the Allianz Stadium.
Paul Pogba, meanwhile, is no closer to a return from his thigh injury, with Solskjaer revealing that he does not expect the United midfielder to play again this month.
Pogba has been sidelined since the 3-3 draw with Everton at Old Trafford on 6 February.
“Paul is recovering well,” Solskjaer said. “He's starting the treatment but it will still be a few weeks. He won't be playing in February, that's for sure, it's still a few weeks before we see Paul definitely.”
Shola Shoretire, a 17-year-old winger recently called up to United’s first team squad from the Under-23s, has been included in the travelling party alongside Amad, the recent £37m signing from Atalanta who is yet to make his debut for the club.
Manchester United travelling squad to face Real Sociedad: De Gea, Henderson, Grant; Bailly, Lindelof, Maguire, Shaw, Telles, Tuanzebe, Wan-Bissaka, Williams; Amad, Fernandes, Fred, James, Mata, Matic, McTominay, Shoretire; Greenwood, Martial, Rashford.