The confrontation, which occurred around dawn yesterday in the town of La Realidad, appears to have been sparked by a dispute over transportation in the densely rainforested region.
The skirmish apparently erupted following a standoff over possession of a car and access to a road linking various communities in the remote region.
"There is one person dead -- a member of the Zapatista autonomous council -- and 11 people injured," an anonymous Chiapas government official told AFP.
A meeting has been scheduled between the two groups to try to resolve the conflict, mediated by local human rights officials.
The EZLN came to prominence in the early 1990s as an armed group defending indigenous people in Chiapas, a region with some of Mexico's highest rates of poverty and illiteracy.