Those detained on suspicion of death by negligence include the principal of the Tel Aviv-based pre-military academy, Israeli media report.
The nine females and one male who died were swept away on a hike in the Negev desert following torrential rain.
Israeli PM Benjamin Netanyahu said the country was in mourning at their loss.
“The State of Israel grieves for the promising young lives that were cut off by the grave disaster in the Arava [region]. We embrace, with pain, the grieving families, and pray for the speedy recovery of the wounded,” he said.