Olinala Mayor Eusebio Gonzalez said the takeover began Saturday after about 100 people stormed a house where the four presumed kidnappers were hiding and killed the suspects by burning the building.
He said nearly 700 residents had since been taking turns policing entry into the town by barricading streets and installing checkpoints.
Gonzalez said the taxi driver's killing was the latest in a series of violent attacks and Olinala residents are demanding more protection from criminal gangs.
Gonzalez said the Guerrero state governor has promised to increase help to battle drug crime.
"We're looking to establish order. The governor is aware of the situation and wants to improve the situation," Gonzalez said. "People feel like there isn't another way."
Known for its artisanal lacquered boxes and quaint colonial-style streets, the town's vigilante unrest erupted at the taxi driver's funeral when rumors circulated that a second driver had been kidnapped.
"Things got really ugly," said Paola Rosendo, an Olinala resident.
Rosendo, a 50-year-old artisan, said tourism has decreased sharply over the last few years, forcing artisans to leave town in order to sell their crafts.
Eduardo Gallo, a respected Mexican anti-crime activist, said Olinala is just the latest in a series of towns where people have taken up arms to combat organized crime in frustration over the government's inability to control drug violence.
"People took over in order to prevent authorities' collusion with criminals," Gallo said.
At least two towns in the western state of Michoacan have formed their own armed guard forces and thrown up roadblocks to keep out criminals. Towns in northern Mexico also have taken similar measures.