The left-back had to be replaced in the first half of Wednesday's 1-0 win over Brentford after picking up what appeared to be a hamstring issue.
Man United are yet to reveal the seriousness of the damage, but Ten Hag said during his press conference on Friday that the England international would be missing against Everton.
There is positive news on the injury front, though, with Christian Eriksen set to return to the squad for the first time since picking up an ankle issue at the end of January.
Eriksen has been back in training for the Red Devils this week and has done enough to convince Ten Hag that he can make his return in the contest with Sean Dyche's side.
"Luke Shaw is not available for tomorrow. We have to see about the progress for the coming week, but the good news is Eriksen is back in training and he will be in the squad," Ten Hag told reporters.
Eriksen suffered his injury in a late challenge from Reading forward Andy Carroll, and Man United's head coach has said that he was "so angry about the tackle".
"I was so angry about the tackle. He was away, we felt we had lost him for the whole season, but he worked very well," added the Dutchman.
"The medical department did very well. He's now available for the final stages of the season. At first, it was a really bad tackle and a bad injury. He's ahead of schedule, so we're happy with that."
Aside from Shaw, Man United have not suffered any fresh problems following their 1-0 victory over Brentford, which moved them into fourth position in the Premier League table.
"No. Shaw is unavailable, Eriksen is back in the squad, for the rest we have a squad that is ready to play," said Ten Hag when asked about the rest of his squad.
Donny van de Beek, though, is out for the season with a knee injury, while Tom Heaton and Alejandro Garnacho are still on the sidelines through injury.
Man United will also again be without Casemiro, with the experienced midfielder serving the final game of his four-match suspension, having missed the recent games with Fulham, Newcastle United and Brentford.