"He is out for the start of the season," he told United's website.
"He came from the World Cup with the injury and the time he had to rest on holiday was not enough to resolve the problem.
"I don't know how long he will be out for."
Mourinho could have done with Matic's defensive capabilities on Saturday as his side were well beaten by their fierce rivals in front of more than 100,000 spectators in Ann Arbor, Michigan.
Swiss forward Xherdan Shaqiri, a recent signing from Stoke City, marked his Liverpool debut with a brilliant bicycle kick that capped the scoring.
Sadio Mane had given Liverpool the lead with a penalty just before the half-hour mark before Andreas Pereira equalised with a stunning free kick minutes later.
Substitute Daniel Sturridge made it 2-1 after 66 minutes before Sheyi Ojo scored Liverpool's second penalty of the game after Andrew Robertson went down in the box.
(Reporting by Andrew Both; Editing by Peter Rutherford)
