The camp, where some 1,500 workers live, was inundated after heavy rains caused the Mzymta River to breach the dam Wednesday morning, R-Sport reported.
No one was injured, the regional office of the Emergencies Ministry said in a statement.
Repairs to the dam have already begun.
The camp is in the village of Esto-Sadok near the Krasnaya Polyana mountains where skiing and other events will be held.
Celebrity Breakups and divorces of 2014 [PHOTOS]