The defenders picked up back and ankle injuries respectively in the first half of United’s 3-1 Premier League victory at Fulham on Saturday, while midfielder Tom Cleverley also had to be withdrawn at the break with double vision.
However, while Cleverley has recovered to make the trip to the Basque Country, manager David Moyes confirmed on Monday that Evans and Rafael have been left behind in Manchester.
"We haven't had a lot of injuries - I think it’s the best Manchester United have been in that respect for a while," said the Scot.
"But we did pick up three on Saturday, which is very rare - especially by half-time.
"Two of them haven’t travelled, Jonny Evans and Rafael, so they're not with us."
United sit top of Group A with seven points from their three games and beat Sociedad 1-0 in last month's reverse fixture at Old Trafford.
The Premier League title holders are also on a seven-match unbeaten run in all competitions - a streak Moyes is keen to extend at Anoeta.
Sociedad prop up the pool having lost all three of their matches so far, although Moyes is taking nothing for granted ahead of Tuesday’s clash as he seeks to reach the 10-point mark widely regarded as the threshold needed to ensure qualification.
"I feel we're playing better and getting some good results to go with it," he added. "Long may that continue.
"I have a lot of respect for Sociedad. We have to play well if we’re going to get those 10 points, which will get us over the line.
"We've got ourselves into a good position in the group and we have to try to maintain that."
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