Authorities have yet to confirm any deaths.
The alleged confrontation came hours after the federal government told the "self-defense" militias to lay down their arms and go home after a year-long struggle against the Knights Templar gang in Michoacan state.
Vigilante spokesman Estanislao Beltran told AFP that a military convoy arrived in the community of Cuatro Caminos early today to seize their weapons.
Beltran said the shooting took place after residents blocked the road in protest to demand that the soldiers return the guns to the militia
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Two other people, including an 11-year-old girl, were also hit and died on their way to a hospital, he said, adding that he witnessed the shooting.
Attorney General Jesus Murillo Karam told the Televisa broadcaster that the disarmament and "the restoration of legal order have begun" in the troubled state.
But Beltran said the vigilantes would not abandon their weapons.
Civilians first took up arms in February 2013 to oust the Templars from the region, saying local police were either colluding with gangs or unable to deal with crime.
The unrest in the agricultural state has become the biggest security challenge of President Enrique Pena Nieto's 13-month-old administration, undermining his pledge to reduce violence in Mexico.