Sanchez went down with the problem at the start of the second half and was replaced by full-back Diogo Dalot.
United rallied after Sanchez’s departure, turning a 1-0 scoreline to a 2-1 lead and eventually winning 3-2 thanks to Romelu Lukaku’s late winner.
The Chilean was seen limping on his way out of Old Trafford on Saturday evening and Solskjaer fears he may have suffered ligament damage.
“We don’t know yet,” Solskjaer said, when asked how severe Sanchez’s injury was.
“We haven’t checked it too much. It might be the ligaments. It was a bad knock on his knee. We’ll do a scan tomorrow.
“Hopefully it won’t be too bad but we don’t know until we’ve done the scan.”
Sanchez has struggled for form and consistency since joining United from Arsenal in January 2017.
The 30-year-old is not considered a first-choice starting player under Solskjaer, who has tended to prefer Anthony Martial, Marcus Rashford and Jesse Lingard in his front three.
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