Police claim that "radical groups" contributed to the violence, saying what happened in Oaxaca state "was practically an ambush".
Protesters have launched rockets at riot police in Mexico, amid new demonstrations against education reforms that left eight people dead on Sunday.
Another 100 people were injured when police tried to stop a highway from being blocked in the southern Oaxaca state at the weekend.
Teachers and their supporters took to the streets again on Monday, carrying a makeshift coffin, amid allegations of police repression.
Speaking on local radio, federal police chief Enrique Galindo attributed the violence to "radical groups", saying that few teachers had been involved.
Mr Galindo said about 2,000 protesters had been on the streets on Sunday, some of them carrying gasoline bombs and powerful fireworks.
He ordered armed officers to move in when gunshots had been confirmed.
"It was a radical change of scene," Mr Galindo said. "It was practically an ambush."
Speaking at a news conference, Mr Galindo showed pictures of a police helicopter that had been hit by bullets.
He also said three federal police officers were being held in Nochixtlan.
State prosecutor Joaquin Carrillo said seven civilians - none of them teachers – had died of bullet wounds on Sunday.