The unidentified student opened fire Wednesday morning at the bilingual Colegio Americano del Noreste, according to Aldo Fasci, a security spokesman for the state of Nuevo León. Conditions of the wounded were unknown.
The school accepts students from preschool to the secondary level, according to its website.
The teacher is 27 years old; the shooter and the three classmates who were wounded are 14 and 15 years of age, according to Fasci.
The shootings were reportedly captured on a school surveillance camera, he said.
Monterrey is about 140 miles south of Laredo, Texas.
By Rafael Romo, Ana Melgar and Layla Santiago