Original description as Cynodonichthys tenuis:
- Meek, Seth Eugene. 1904. "The fresh-water fishes of Mexico north of the isthmus of Tehuantepec". Field Columbian Museum Publication. pp. 1-252 (ffm00159)
- Rivulus godmani Regan, 1907, with type locality at Guatemala. Determiner: Huber, 1992
- Rivulus myersi Hubbs, 1936, with type locality at 3 kilometers south of Progreso, Yucatán, Mexico. Determiner: Huber, 1992
- Rivulus hendrichsi Alvarez & Carranza, 1952, with type locality at Salto de Agua, Chiapas, southeastern Mexico. Determiner: Huber, 1992
Conservation: Rivulus tenuis is not evaluated by the international union for the conservation of nature in the iucn red list of threatened species.