Can a herniated disc cause neuropathy?

Yes: A neuropathy is disease of a nerve root. If a herniated disc presses on a nerve root, it will cause symptoms. However, not all disc herniations cause neuropathy. AND, not all symptoms of neuropathy are caused by disc herniations. Often, symptoms will resolve with supportive care.

Agreed: It may be semantics, but when a disc herniation occurs, it presses on a nerve root and not a nerve. We call this radiculopathy. Neuropathy occurs further from the spine and often implies a non-compressive origin (although it can be compressive).

Yes it can: Herniated disc can cause neuropathy by pressing on the spinal chord which will cause neuripathy