Thursday’s progress to the Europa League semi-finals came at a cost as the duo were forced off 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 quarter-final second leg went to extra-time.
The veteran striker’s knee buckled and Mourinho fears the worst when it comes to the injuries sustained by his top scorer and influential defender.
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 finish.
“We are in trouble,” said Mourinho. “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 said he was “OK” 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 OK.”
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 will start.
“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.”
Meanwhile, Mourinho believes it would be illogical for Rashford to play for England U21s this summer, saying it does not make sense for the teenager to “drop levels”.
There has been precious little let-up for the 19-year-old since he broke onto the scene so remarkably 14 months ago.
Rashford’s outstanding displays for United saw him fast-tracked into the England squad for Euro 2016 and there is now talk of him heading to this summer’s U21 European Championship.
The Football Association has yet to make a concrete decision one way or another on the matter and will pick it up with United towards the end of the season.
Rashford’s availability was always going to be down to circumstance and Mourinho believes the fine way he is ending the campaign means the striker has moved beyond the under-21s.
“I don’t want to go in that direction,” he said when asked about the championships in Poland.
“I just feel that when a player reaches a certain level, it doesn’t make a lot of sense to drop levels.”