Nerve scaffolds are described that include a tubular outer housing fabricated from a biocompatible polymer, within which are disposed a plurality of carbon nanofiber yarns. The carbon nanofiber yarns, which can be separated by distances roughly corresponding to an average nerve fiber diameter, provide surfaces on which nerve fibers can regrow. Because the proximate carbon nanofiber yarns can support individual nerve fibers, a nerve can be regenerated with a reduced likelihood of undesirable outcomes, such as nerve pain or reduced nerve function.