The protests in the impoverished southern states of Oaxaca and Guerrero occurred despite the deployment of federal police and troops to ensure people can cast their votes across the country.
A radical teachers union is putting pressure on President Enrique Pena Nieto to withdraw a landmark education reform aimed at improving the country's lackluster school system.
In the Guerrero town of Tixtla, protesters angry at Pena Nieto's handling of the alleged killing of 43 college students in September of last year burned election material, forcing authorities to cancel the vote in the municipality of 40,000 people.
Despite the protests, election authorities said 99.95 percent of the polling stations were successfully installed for Mexicans to choose 500 members of the lower chamber of Congress, around 900 mayors and nine governors.
After casting his ballot in Mexico City, Pena Nieto said there were reports of "isolated incidents" but that it was "rather satisfying to know that the great majority of polling stations were installed.