Gisela Mota, mayor of the Mexican city of Temixco, was gunned down at her house on Saturday only one day after taking office.
Soon after the shooting, police located a car of suspects who then opened fire on them. Two were killed and three arrested, including a 32-year-old woman, an 18-year-old and a minor.
In a separate car, police say they found a number of weapons and ski masks.
Governor of the state of Morelos Graco Ramirez said the murder was linked to organised crime, though did not specify the particular group involved.
He also announced new security procedures for all mayors in the state.
According to the Association of Local Authorities of Mexico, almost 100 mayors have been killed across the country in the last decade, largely at the hands of organised criminals.
Located just south of Mexico City, Temixco has been a popular tourist destination, but Morelos has seen an increase in kidnappings, extortion and murder by gangs in recent years.