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.

New Zealand, who set a new record in the professional era by winning all 14 of their Tests in 2013, won team of the year for the seventh time.
And Steven Hansen was named coach of the year for the second time in a row.
"This is fantastic recognition of a very special team," said New Zealand Rugby chairman Mike Eagle.
Kieran Read is the third New Zealander to win the IRB world player of the year award. Dan Carter triumphed in 2005 and 2012, while Richie McCaw won the award in 2006. 2009 and 2010
"We are very proud of what Steve, Kieran and the team have achieved in 2013 as they have worked hard to be the best."
Read, 28, who has played 61 Tests for New Zealand, was chosen ahead of countryman Ben Smith, Wales' Leigh Halfpenny, South Africa's Eben Etzebeth and Italy's Sergio Parisse.
He is the third New Zealander to win the award, following Dan Carter in 2005 and 2012 and Richie McCaw in 2006, 2009 and 2010.
"I'd like to congratulate Kieran on his award as it is well deserved," said Hansen.
"He has been outstanding and has been a major contributor all season. It's been a big year and I'm incredibly proud of what the boys have achieved.
"It's certainly special to have the All Blacks named for all three awards so it's important that we thank and acknowledge all those behind the team."
The winners of the three awards were picked by a panel chaired by Australia's 1999 World-Cup winning captain John Eales and made up of Will Greenwood, Gavin Hastings, Raphael Ibanez, Francois Pienaar, Agustin Pichot, Scott Quinnell, Tana Umaga and Paul Wallace.
New Zealand's 14th win of 2013 came against Ireland late last month as they secured victory with a converted injury-time try to edge the autumn international 24-22.
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.
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New Zealand number eight Kieran Read has been named world player of the year as the All Blacks dominated the International Rugby Board awards.