The interior secretary of Michoacan state told the Milenio television network that five bodies have been found so far. Pascual Sigala said emergency personnel were still working to find nine people reported as missing.
Unusually heavy rainfall swelled the Cutio River and sent a wave of water into the town of Periban on Sunday.
The muddy surge was so strong it carried away vehicles and trees.
Periban is located in a forested, mountain zone known for its avocado groves.