The England international pulled up with a possible hamstring injury with only a few minutes remaining in the first half and the last-16 first leg tied 0-0.
Lingard went back onto the pitch to test out the problem, but it quickly became apparent he would be unable to continue.
Just before the half ended, Lingard was taken off with Alexis Sanchez introduced in his place.
Lingard's injury will come as a blow to United, with the 26-year-old having made himself a big part of his side's resurgence under caretaker manager Ole Gunnar Solskjaer.
Since the Norwegian took charge in December, Lingard has four goals and three assists for the Red Devils in all competitions.
United are also facing a difficult run of fixtures that will test the squad's depth.
Anthony Martial also went down with a possible hamstring injury in the first half of Tuesday's game, though the Frenchman was able to continue.
However, Martial was taken off at the half in favour of Juan Mata, though it was not clear if that substitution was related to the injury.
"You don't know," Manchester United manager Ole Gunnar Solskjaer said of the two injured players after the match. "Muscular injuries, hamstring and groin. We'll need a couple of days to assess them."
Solskjaer also admitted that losing his two stars would be a blow for the team's playing style.
"That's the reality," he said. "Jesse and Anthony are big parts of our squad. They've played really well.
"Second half we didn't have so much movement and pace to get in behind. Juan got on the ball for us and created a few bits. We need to find a different way to play when Anthony and Jesse are out."