The bodies were found at the bottom of a deep gully near the town of Queseria, on the border between the states of Jalisco and Colima, said Colima Governor Jose Ignacio Peralta.
"Some of them are already in an advanced state of decay. Some are practically just skeletons," he told journalists.
"An investigation will have to be carried out. We have counted 10 so far, but that's a preliminary report."
The border region between the two states is controlled by the powerful Jalisco New Generation drug cartel.
It is fighting a turf war with the notorious Sinaloa cartel.
Both are known for murdering their enemies and ditching the bodies in remote areas.
Mass graves, sometimes containing hundreds of bodies, have become all too common in Mexico as drug cartels and the army fight violent battles over the lucrative narcotics trade.
Recently discovered mass graves in the eastern state of Veracruz -- another state where Jalisco New Generation is seeking dominance -- contained at least 242 bodies, according to investigators.
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