Just to dovetail @jcarpenter1 's advice.
1. Create a new module. Call it something like "Not For Student Eyes." Move the discussion into that module. Do not publish the module.
2. Make sure that "Discussions" does not appear in the students' course navigation bars. If it does, go into settings and then navigation. You'll need to disable "discussions."
3. I believe that students will still be able to access their own response(s) through Grades, but not the rest of the discussion thread.