The accident occurred on Sunday in Mexico City's main Zocalo plaza and the injured were taken by paramedics to hospitals, the secretariat said.
The victims mostly sustained bruises and not "life-threatening injuries," the secretariat said.
Political and grassroots organizations staged peaceful protests in the capital on May Day and no serious incidents were reported, the secretariat said.
Metropolitan Police officers surrounded a group of "self-proclaimed anarchists" at the Monument of the Revolution, the secretariat said.
Police received a tip that the young people planned to disrupt the march by workers, officials said.
The group spoke with police and "they were allowed to rejoin the march," the secretariat said.
The young people left behind three Molotov cocktails fashioned out of beer bottles, two cans of spray paint, several large stones and a container filled with nearly a gallon of gasoline, the secretariat said.
Mexico City's government deployed about 3,000 police officers to provide security during the May Day demonstrations.