Reports say that police fired on protesters who blockaded roads and burned vehicles in the municipality Nochixtlan in the southern state of Oaxaca.
Federal Police described the protests as the most aggressive in the region, saying that the protesters even took a police officer hostage.
In the municipality of San Pablo Huitzo, authorities said violence continued for hours, and in the western state of Michoacan, and closed shopping malls, train lines and bus services had to be canceled.
The demonstrators burned a federal police buildings in the city of Oaxaca, police were forced to remove people who were blocking a main road in Tehuantepec.
National Coordinator of Education Workers (CNTE) and Western fighting the imposition of mandatory teacher testing, which is part of a series of government reforms.
It is also angry at the arrest of union leaders.
He says federal prosecutors have set up illegal financial network to pay for the protests and their pockets, using this between 2013 and 2015, they also effectively seized control of the salaries of teachers in Oaxaca.
According to Isabel Garcia, a member of the political committee of the Union, three people support the protests were killed. She did not confirm whether they were teachers.
An official at the state police officer died in the clashes.
The federal government said in Mexico on Sunday night that the 21 federal agents were injured, three of them by fire. She said the federal police officers involved in the operation were not carrying guns.
The statement said that “the attacks with guns came from people outside the blockade, which was launched on the population and the federal police.”