Radical teachers opposing Mexico's program for evaluating and testing teachers blocked exam sites and cut off the hair of some who showed up.
The Education Departments says Sunday's attacks were the work of "violent and intolerant groups." It pledged on Monday to push ahead with testing, which has been interrupted in the states of Chiapas, Oaxaca and Michoacán.
One woman who was to take an exam for hiring first-time teachers said she was surrounded by a crowd who grabbed handfuls of her hair and cut it off. Photos showed at least two other people getting involuntary haircuts in Chiapas.
The protesting teachers say recently implemented tests don't truly evaluate their skills. Some Mexican teachers inherit their positions from relatives and hiring or promotion decisions are sometimes controlled by unions.