The right-back limped off early during United's 0-0 draw with San Jose Earthquakes, and Mourinho said after Wednesday's penalty-shootout victory over AC Milan that Valencia may miss the start of the Premier League season.
"Antonio Valencia is injured, and I think he will be injured for the beginning of Premier League season," per Dan Gibbs of the Express. "Diogo Dalot is also in a recovering phase, and he will not be ready for the beginning of the Premier League."
United's 2018-19 Premier League campaign kicks off with a home clash against Leicester City on August 10.
Valencia, 32, is a vital component of Mourinho's side. He started 31 Premier League games for United last term and was one of the club's most consistent performers.
The Portuguese manager does have back-up to call on, but it is of variable quality.
Matteo Darmian is one possibility, but Mourinho revealed the Italian wants out of Old Trafford, per Gibbs: "Matteo wants to leave, and I think when a player wants to leave, if the right offer arrives, you have to try to be human and let the player follow his instinct. But not at any price, and until now, the offers we got for Matteo are not even close to being accepted."
Ashley Young is also an option, but he is more comfortable on the left flank and has yet to return from his holiday after playing a key role in England's run to the 2018 FIFA World Cup semi-finals.
Valencia's absence could have been a chance to give new signing Dalot an early opportunity to prove his worth.
The 19-year-old was signed for £19 million from Porto in June, and Mourinho called him the "best young full-back in Europe," per BBC Sport's Simon Stone.
However, he is sidelined until September, per injury analyst Ben Dinnery:
Ben Dinnery @BenDinnery
Mourinho confirms new signing Diogo Dalot will be our for another two months:”He is injured; we knew that [before] but we didn't want to lose him because of that. He is recovering really well. He will not be ready for the start of the season, but we think he will for Sept." #MUFC
United have endured a mixed pre-season, and Valencia's injury is one of the low points.
The Ecuador international is a crucial player for United, and Mourinho will hope his captain returns from his calf injury as soon as possible.