Thursday's quarter-final second leg against Anderlecht at Old Trafford, which United won 2-1 in extra time on the night for a 3-2 triumph on aggregate, saw striker Ibrahimovic hobble off after landing awkwardly towards the end of normal time and defender Rojo depart on a stretcher in the first half.
Asked about the condition of the pair, Mourinho said: "I want to wait, but my feeling is not good for both. I want to wait and try to be optimistic, but I am not."
Rojo's injury comes at a time when United already have Phil Jones (foot) and Chris Smalling (knee) sidelined.
When it was put to him that he was facing a significant lack of options at centre-back, Mourinho mentioned Daley Blind - Rojo's replacement from the bench - before suggesting Jones and Smalling needed to be "brave".
Mourinho, who earlier this season made an apparent criticism of Smalling's pain threshold, said: "We have Daley Blind, who has experience in the position, and I think it is time for Jones and Smalling to be brave - to risk.
"Because for the team you have to do everything, that is the way I think. You cannot do miracles, so miracles I don't expect, but they have to try to do everything to accelerate the process.
"They have injuries, and even with a crazy mentality, they cannot play Sunday (at Burnley in the Premier League). But with a special spirit, you can (come back) sooner than expected. So instead of mid-May, it could be the beginning of May, this kind of acceleration of the process."
Read the full article on eurosport.co.uk: Mourinho fears worst over Ibrahimovic and Rojo injuries