After seizing alleged collaborators of the gang, including the mother of the leader "El Tequilero", the locals have recorded video messages for the gang.
"In return for my husband's life, I will deliver your mother," says the kidnap victim's wife in one video, which has been broadcast on local TV.
Police have been sent to the village.
"We have your mother here, mister known as El Tequilero," says Yadira Guillermo Garcia, whose husband, an engineer, was seized by the gang, addressing the gang leader.
"I request an exchange.... I want him safe and sound."
In another video, residents of San Miguel Totolapan, carrying guns, explain that they have suffered for too long from the violence and intimidation meted out by El Tequilero and his gang, which is feared for carrying out mass kidnappings.
"They have humiliated us, they have killed our families and we won't let it happen again," one of them says.
Police have been trying to track down El Tequilero, whose real name is Raybel Jacobo de Almonte, for weeks now.
At the end of November, police used helicopters to search the mountainous area in Guerrero state where he is believed to be hiding but failed to catch him.
The governor of Guerrero state, Arturo Astudillo, said more than 200 police officers and soldiers had been sent to San Miguel Totolapan to defuse the stand-off.
He said the villagers had released five of the people they were holding but that El Tequilero's mother was not among them.
Guerrero state officials said that a team had been set up to negotiate between the vigilantes and the gang.
"The goal of the team is to ensure that no injury is done to the missing person, nor to the mother of the head of the Tequileros gang, who has apparently been taken by the self-defence forces," a statement read.
Guerrero state is a hotbed of gangs and violent crime, where local gangs fight for control of the opium trade, and disappearances and kidnapping for ransom are common.
In a number of towns and villages, residents have created vigilante groups in response, but human rights groups say these have only further contributed to the spiral of violence.
Vigilantes in a Mexican village have seized the mother of a local gang leader and proposed swapping her for a kidnap victim taken on Monday.