The body of the unnamed woman was found at a morgue in the central city of Toluca about 60 kilometres (40 miles) southwest of Mexico City after she was kidnapped on September 13th, Foreign Minister Jose Manuel Garcia Margallo told radio Onda Cero.
Her captors had forced her to withdraw money from bank machines and demanded money from her family to ensure her release, he added.
"An amount was paid, although much lower than what they had asked, and we were convinced that it would be a matter of time before she appeared safe and sound. Unfortunately things did not turn out that way," the minister said.
"It is very sad news and totally unexpected," he added.
The woman's husband and her cousin Gorka, one of Villar's sons, had travelled to Mexico along with two Spanish police officers to try to secure her release, the minister said.
He did not say how much money the kidnappers had demanded but Spanish media said that 200,000 Mexican pesos (9,000 euros/$10,000) had been asked for to secure the 36-year-old's release.
The woman was kidnapped as she withdrew money from a bank machine in Santa Fe, a major business district in the west part of Mexico city which consists mainly of highrise buildings surrounding a large shopping mall, daily El Mundo reported.
Villar, who has been president of the Royal Spanish Football Federation since 1988, is a former Athletic Bilbao and Spain midfielder who has sat on the executive committee of world football ruling body FIFA since 1998.