The incident occurred Thursday night at the camp in Ixtapaluca, a city in Mexico state, the Mexico state Attorney General's Office said.
About 90 children and teenagers had been camping in the area since Monday, the AG's office said.
The camp director notified the prosecutor's office in Ixtapaluca Friday morning that about a dozen armed people had attacked the camp the night before, the AG's office said.
"The armed group held the campers for several hours. During the time they were at the place, they sexually abused seven minor females and beat several young men," the AG's office said in a statement.
The assailants stole personal items and two vehicles before leaving the camp, prosecutors said.
The victims will be provided with legal, medical and psychological assistance, Mexico state Gov. Eruviel Avila said.
The perpetrators will be found and given "punishment that makes an example of them", the governor said.