Leishmania (Mundinia) procaviensis is a parasitic kinetoplastid that was first isolated from a rock hyrax in Namibia in 1975. We present the complete genome sequence of Leishmania (Mundinia) procaviensis isolate 253, strain LV425, sequenced using combined short- and long-read technologies. This genome will contribute to our understanding of hyraxes as a Leishmania reservoir.