Shaw suffered an injury in training this week which will force him into the treatment room alongside midfielder Mason Mount, who is
expected to miss up to six weeks of action as a result of a hamstring problem.
Despite initial hope that Shaw's injury may not be as serious, Ten Hag has now confirmed he does not expect to see the left-back return before Mount.
"We can't do that [put a timescale], it's personal these days," he explained. "Luke will be longer than Mason I think."
United are already without their only other natural left-back Tyrell Malacia, who is still several weeks away from making his return.
"It will also take a few weeks before he will be back," Ten Hag said of Malacia. "Definitely, we have the solutions in our squad to cope with that. We thought before the season about this scenario, it could happen, you hope to avoid. But if it happens you have to be ready for it."