The containers, holding more than 4,000 fish, apparently stood out in the summer sun for more than 14 hours.
The creatures had been shipped from China and were intended for a giant, newly built aquarium in the city.
The aquarium's administrators said the tragedy inflicted damages of nearly $500,000.
The official opening of the "Sochi Discovery World Aquarium" is planned for the second half of September. No confirmation on reports of a name change to "Sochi Discovery World Baths."
-- RFE/RL's Russian Service