Authorities in Mexico say 43 people were injured during Saturday's clashes between police and demonstrators in Oaxaca. About 150 people were arrested.
On Sunday, Oaxaca Governor Ulises Ruiz said the full weight of the law will fall on those responsible for acts of vandalism during the demonstration.
The governor's resignation is one of the demands of the protesters.
Some protesters threw firebombs and fireworks, setting fire to several buildings. Police responded with teargas and water cannons.
Oaxaca has been shaken by demonstrations since May. The protests began when teachers walked off the job demanding better pay and school funding.
The protests became violent when activists critical of Governor Ruiz joined the demonstrations.
The activists accuse Ruiz of rigging the 2004 election that brought him to power. They also complain he had the police use heavy-handed tactics to break up the teachers' strike.