Thursday's progress to the Europa League semi-finals came at a cost as both Ibrahimovic and Marcos Rojo suffered nasty-looking injuries during the 2-1 extra-time win over Anderlecht.
Rojo was taken off on a stretcher after seemingly sustaining a knee injury, and Ibrahimovic landed awkwardly just before the end of normal time in the quarter-final second leg.
The 35-year-old striker's knee buckled, with reports on Friday evening suggesting he could be out until 2018 due to cruciate ligament damage, and Mourinho is fearing the worst when it comes to the injuries sustained by his top scorer and influential defender Rojo.
Both are being assessed to see how long they will join Juan Mata, Chris Smalling and Phil Jones on the sidelines for at a crucial point in the season, with United chasing Europa League glory and a top-four Premier League finish.
"We are in trouble," Mourinho said. "We are in trouble.
"In this moment, Eric Bailly played six matches in a row, and we lost Marcos Rojo, we don't have Jones or Smalling, we are in trouble and now we lose Zlatan too.
"But in attack, we have options and (Wayne) Rooney is coming, and let's see if Mata can also return before the end of the season, let's see what happens."
Rojo told reporters he was "okay" while limping heavily through the post-match mixed zone, and Luke Shaw said Ibrahimovic did not seem in too bad a state in the dressing room.
"I knew it did not look so good on television, but he seems to be in good spirits," the left-back told Sportbladet.
"He walked around in the dressing room. I do not know the extent of his injury, of course, but I saw him in there and he was optimistic.
"Hopefully it is not too bad for him. We hope it is not too serious and he seems okay."
The onus will be on Marcus Rashford and Anthony Martial to step up in Ibrahimovic's absence.
Rooney is another attacking option after returning to the bench against Anderlecht following ankle issues, with Mourinho backing his captain to have a big influence in the closing weeks of the campaign.
"He has a good mentality, he is a fighter," the United boss said ahead of Sunday's trip to Burnley, where he confirmed Ander Herrera would return to the starting line-up.
"He is a strong man, even if he is not in the best condition, even if he is not in the level of sharpness that you need to play high-level football, but he has the experience and character, so he has to.
"Now we need absolutely everyone, now I even have to think that Axel Tuanzebe, has to go to the under-something World Cup in Korea, because maybe Axel has to come now, now we need everyone."