Sanchez was omitted from the Manchester United squad which beat Young Boys on Wednesday.
But in training on Thursday, the Chile international injured his hamstring as United prepared for this weekend’s clash with Southampton.
And speaking in his pre-match press conference, Mourinho confirmed Sanchez is set for a lengthy spell on the sidelines.
He told reporters: “No scans yet.
“But the player is experienced, the player knows what the injury is and also from the top of my experience, just the painful scream and the way the injury happened I know it’s going to be for a long time.
“Is not the little muscular injury that in one week or 10 days the player is ready, is for me and also for Alexis, the feelings before the scans is that the grade is different than the Lindelof one and the Lindelof one was not an easy one so I think Alexis has what I used to call an aggressive muscular injury.”
Sanchez’s injury means he will miss games against Southampton, Arsenal, Fulham, Valencia, Cardiff, Huddersfield, Bournemouth and Newcastle.
Alexis Sanchez could be back in time for United’s trip to Tottenham on January 13.
Sanchez has had a poor season and been unable to command a place in Mourinho’s starting XI in recent weeks.
And the United boss defended his selection decisions.
“The first thing I can say is that in every club, when a player is not playing it is a simple manager’s decision,” he said.
“In our club when a player does not play it is always because of the player is not behaving and has disciplinary issues.
“Of course that is not the case again.”
Yet the Chilean’s absence until the New Year could fuel speculation that he is set to leave the club.
Paris Saint-Germain are said to be interested in the player, while a return to Spain – where he previously played at Barcelona – may also suit the forward.
United signed Sanchez from Arsenal in a swap deal for Henrikh Mkhitaryan in January this year.
Yet the move proved to be less than fruitful for the ex-Gunners superstar, who scored just three goals in the remainder of the season.
He has scored once for United this term and has started just seven games.