Preliminary reports were that the student entered the school and fired at a teacher before apparently shooting himself, the mayor said.
"It's a tragedy. It's very, very sad that a boy of 11 can come to school with two guns", Mr Zermeno told local television.
"He appeared to have been influenced by violent video games".
When the 11-year-old failed to return to class after 15 minutes, the teacher went looking for him and the boy opened fire using two handguns, Marquez added.
Riquelme said the boy had not shown behavioral problems, but had told classmates that "today was the today", and talked to them about the first-person shooter video game "Natural Selection".
Though homicides have reached record levels in Mexico during the past two years, school shootings are unusual.
The boy had talked to classmates about the game, said Riquelme.
Police are still investigating but believe the boy was between eight and 10 years old, said Lieutenant Adelaido Flores, as panicked parents gathered outside the Cervantes elementary school and officials evacuated the building.
The Director of Municipal Public Safety, Primo Francisco García, confirmed to local media the death of a teacher and a student.
The wounded - five pupils and a physical education teacher - were taken to a local hospital, where they were in stable condition, said Governor Miguel Angel Riquelme of the state of Coahuila, which borders the United States.