Leishmania (Mundinia) martiniquensis is a kinetoplastid parasite that was first isolated in 1995 on Martinique. We report the first complete genome for Leishmania martiniquensis from Asia, isolate LSCM1, strain LV760, which was sequenced using combined short-read and long-read technologies. This will facilitate greater understanding of the evolution of the geographically dispersed subgenus Mundinia.