The Manchester United pair were both forced off during the 2-1 extra-time win over Anderlecht, as Mourinho’s men reached the Europa League semi-finals on Thursday.
Ibrahimovic fell awkwardly as he challenged for a high ball just before the second half finished, with the 35-year-old mooted to have injured his Achilles.
Rojo, meanwhile, was stretchered off earlier in the game after a challenge on his knee.
United do not yet know the full extent of the injuries, but Mourinho is not optimistic and is certain neither will feature in Sunday’s Premier League clash against Burnley.
"I don't think they are easy injuries, but I prefer to wait for all the tests to be done tomorrow,” he said.
"I want to wait. My feeling is not great for both. I want to be optimistic, but I'm not.
"I can't say any more than that, I am not a doctor.
"But even with a crazy mentality, they cannot play Sunday. But with a special spirit, it can be sooner than expected. Instead of mid-May, beginning of May.”