The protests are reminiscent of unrest that paralyzed the southern city for five months in 2006 and left at least a dozen people dead.
The Section 22 teachers union said 20 protesters were injured during the running clashes, which lasted several hours. Police at the scene said five officers were hurt. Reporter Gildardo Mota of Radio Rama said he was struck on the left leg by a bullet.
The violence broke out in Oaxaca's main plaza as the teachers gathered to protest. The teachers threw rocks and hit police with sticks. Police fought tear gas. It was unclear who fired the live ammunition.
Oaxaca, the capital of the southern state by the same name, is one of the most popular tourist destinations in Mexico because of its picturesque colonial center, Zapotec ruins and surrounding Indian villages known for their arts and crafts.
The protesters also torched a government vehicle and beat the Oaxaca state Public Safety Secretary Marco Tulio Lopez when he tried to call for calm outside the government offices.
Section 22 was the same union that began the 2006 protests. That upheaval began as a teachers strike to demand higher pay but quickly ballooned into a wider movement against then-Oaxaca Gov. Ulises Ruiz, who was accused of rigging his election.
Protesters seized the main plaza for months until federal forces moved in to clear them out.
Section 22 leaders said Tuesday they were protesting a decree that Calderon signed Monday giving parents tax breaks on private school tuition. The union leaders argue the measure undermines Mexico's already struggling public schools. They threatened more protests and roadblocks in response to the police crackdown.
Calderon completed his visit despite the protest, signing several agreements with the state government.
(This version CORRECTS that Calderon's initiative is to give tax break for parents paying private school tuition, not reduce taxes on private schools)