The Ecuadorian pulled up with a muscle problem early on in the dour 0-0 draw with San Jose Earthquakes on Sunday, with his injury later diagnosed as a torn calf.
United get their Premier League campaign underway against Leicester on August 10 and Mourinho has confirmed that he will be without both Valencia and youngster Diogo Dalot as he continues to recover after knee surgery.
That leaves United stretched at the back, with other potential candidates in Victor Lindelof and Ashley Young currently on holiday after their involvement in the World Cup.
"Valencia is injured, you are right," Mourinho explained. "He will be injured for the beginning of the Premier League, Diogo Dalot is also in a recovering phase, he will not be ready for beginning of Premier League.
"Ashley Young is a possibility to play right-back, but is on holiday. I don't know if he fancies to be back for that and put himself to be available for the team or stay on holiday.
"Victor Lindelof is a possibility, he is not a right-back but is a possibility, he starts training next Monday. I will send people to Manchester to train with Victor, it makes no sense for him to come to the United States.
That leaves Matteo Darmian as United's other senior option, but there is no guarantee he will still be at the club by then, having made his desire to return to Italy clear.