Prosecutors said the gang subjected the campers to an ordeal lasting several hours. Seven girls were sexually assaulted and other youths were beaten.
The attackers took cash, cameras and mobile phones and escaped in two stolen vehicles.
The governor of Mexico State, Eruviel Avila, has promised to do everything possible to catch those responsible.
About 90 members of the Christian youth group were camping in tents in the Colibri ecological park near the town of Ixtapaluca, about 35km (22 miles) outside Mexico City.
The attackers burst into the camp at around midnight on Thursday firing shots into the air, the victims said.
The campers were rounded up and held at gunpoint while their belongings were ransacked and some were assaulted.
The park is in a hilly region with no mobile phone coverage so it was some time before the alarm was raised.
Mexican newspapers have questioned why there was not better security at the site.
Mexico gang in youth camp rampage