Mantis does manage privileges both globally and project-wise, with project rights overriding global rights. So the most easy solution for this is to have a project not visible by the ones whose permissions you want to limit and one where they have the rights. Just move the respective issue from the project not visible to the users to the one where they have sufficient permissions.

Also, I do not know if this issue is in the right project. Please correct me if I am wrong.

EDIT: I think I found an issue in my suggestion. I think the users in question should be able to see what other users at the same access level have been assigned issues?