Schultze is remembered for his numerous medical publications regarding neuroanatomical and neuropathological investigations that he performed. In 1884 he was credited with being the first physician to describe a neurological disorder that would later become known as Charcot-Marie-Tooth disease. He also provided an early description of acroparesthesia. In 1891 with Wilhelm Heinrich Erb (1840-1921) and Adolph Strümpell (1853-1925), he founded the journal Deutsche Zeitschrift für Nervenheilkunde.
His name is lent to the eponymous comma tract of Schultze (interfascicular fasciculus), which is a compact bundle of posterior root fibers situated near the border between the fasciculus gracilis (tract of Goll) and cuneate fasciculus (tract of Burdach) of the spinal cord.