The shooting occurred at the Cervantes de Torreón School in the city of Torreón, the city’s mayor, Jorge Zermeño Infante, told reporters.
Preliminary reports were that a child entered the school with two weapons, firing at a teacher before apparently shooting himself, the mayor said.
Four of the wounded were at a nearby hospital, he said. Their condition was unknown.
The Director of Municipal Public Safety, Primo Francisco García, confirmed to local media the death of a teacher and a student.
The school includes students from kindergarten through high school, according to its website.
Coahuila sits on the border with Texas.