The England defender hobbled off after just nine minutes of the contest at Old Trafford, with Mourinho stating after the match that he expected Shaw to have a "big injury".
Shaw is now set for further assessment on his injury and will play no part in United's run-in as they attempt to secure a place in the top four of the Premier League and win the Europa League.
"Luke Shaw is out for the season," said Mourinho ahead of Thursday's Europa League semi-final first leg against Celta Vigo.
"It's an important injury, obviously, but we are still waiting for a second opinion for the medical department to decide what to do.
"He's out for the season, that's confirmed."
It marks further frustration for the 21-year-old, who has been in and out of the first team this season.
Arriving from Southampton in the summer of 2014, Shaw sustained a horrific leg break in a Champions League match against PSV Eindhoven during the 2015-16 season which sidelined him for a nearly a year. Since returning, he has struggled to recapture his pre-injury form, with Mourinho openly criticising his performances and desire to fight for the cause with his persistent injury struggles.
While Shaw is unavailable, United confirmed that Paul Pogba, Phil Jones, Chris Smalling and Eric Bailly – who was also injured versus Swansea – all trained on Wednesday.
"Bailly is ready to play. He is the kind of personality that fights against every problem unless it's impossible he is ready to play," added Mourinho.
"Smalling and Jones are back and Pogba. It's very important in relation to the Europa League, they are on time. We have two matches in one week against Celta, it's important to have everybody back."
Juan Mata was unexpectedly named among the substitutes against Swansea after it was originally thought he could miss the rest of the campaign with a groin injury.
And Mourinho says the Spain playmaker is ready to feature against Celta.
"Mata was injured for a while, but he is ready to play. He is experienced. He is one of the few players that played European semi-finals and finals so it's nothing new to him," said the Portuguese.
"The only risk is that probably he cannot play 90 minutes. That's the risk, if he starts he doesn't finish the game.
"If he comes from the bench it is no problem for him, so he's selected and he can perfectly play."