Shaw has been absent with an ankle problem since the end of April, while Young also missed the end of last season after picking up an injury in the Europa League semi-finals against Celta Vigo.
The duo travelled to America for United's pre-season tour, however, and Mourinho has confirmed that the pair will make their comebacks for the Under-23 team at Leigh Sports Village next week.
"Everybody is fine. The next week, on Monday, in the Under-23s game, Luke Shaw and Ashley Young are playing their first minutes of competition this season," Mourinho told MUTV.
"It is like a pre-season match for them. But it is good news because, when they can play with the Under-23s, it is because the last week they trained with us all week so they are both coming [back]."
United will continue their 2017-18 Premier League campaign away to Swansea on Saturday afternoon.