Lindelof was deemed fit enough to start for the visit of Palace, a dull goalless draw with has increased the pressure on Mourinho's position at Old Trafford.
In the closing stages of the stalemate, the centre-back was in clear pain but with United having made all three of their substitutions, Lindelof played on instead of reducing his team to 10 men.
Mourinho told MUTV: “I believe [he is injured]. I have to believe so.
“I always say this is the period of the injuries. If they are not injured with the national teams, they come to the clubs and are injured.
“He played against Russia three days ago or two days ago, but of course, we need him when he plays.
“He was probably our best player. He was a brave lad, but he probably punished himself.
"I don’t know how long he will be out, but he is a fantastic example.”
Following a troubling maiden campaign at United, the former Benfica defender has been one of the few positives during an otherwise harrowing season for the club.
He has started 11 of the club's 13 Premier League games, missing out just once against Newcastle in October.