Hi Tobias,
I just tested this in 4.14 and Procedural Mesh Component has a shadow on my end. This is what I’m seeing:
I can’t tell if you are playing or in the editor from your screenshot. If you are in the editor, can you make sure that you are in Lit mode?
If you are still having this issue, could you try reproducing it in a new blank project; then upload that project here with repro steps?