The bodies of some victims were reported to have been found several kilometers (miles) downstream from where they disappeared near Autlan in the western state of Jalisco.
“There are nine people missing and seven dead,” local civil protection official Juan Ignacio Arroyo Verastegui told AFP, based on preliminary figures.
Deforestation and a fire earlier this year caused significant damage to the wooded area and could have contributed to the flash flooding, he said.
Dozens of rescue workers were deployed in the area to search for the missing, authorities said.
Mexico is regularly hit by flooding and tropical storms.
Scientists say that climate change is increasing the risk of heavy rain because warmer air holds more moisture.