No. Mothballs, whether made out of naphthalene or para-dichlorobenzene, are insecticides and insect repellents that have no place in a hive containing live bees. Several people have asked if putting the crystals in a bee-proof space—such as a net bag or wire cage—would keep the bees safe from contact. Again the answer is no because it is the inhaled gas that is poisonous.
Both of these chemicals, commonly used to treat clothes moths, work by subliming in a closed environment. Sublimation simply means the material goes straight from the solid state to the gaseous state. The gas, in an enclosed space, builds up to toxic levels that will kill moths and other insects. At lower concentrations, it acts to repel rather than kill the organisms, due to the unpleasant odor.
Since you neither want to kill nor repel your honey bees, you do not want these products in any hive that currently contains bees. Crystals of para-dichlorobenzene are often used in stored bee boxes to keep wax combs free of moths during the winter months, which is fine, but the equipment must be thoroughly aired before being used with live bees. The advantage of para-dichlorobenzene over naphthalene is that the odor will dissipate quickly. On the other hand, equipment treated with naphthalene mothballs may smell nasty for months (or years) to come.
Also, honey meant for human consumption must never be exposed to these products. Not only will it smell bad, but deleterious health effects are known or suspected for each. Both are listed as known carcinogens by the State of California, and para-dichlorobenzene is a neurotoxin. Naphthalene-containing products have been banned by the EU since 2008.
So use para-dichlorobenzene (such as Para-Moth) only for storage of boxes and frames.The best way to control wax moths in active hives is to keep colonies strong and healthy, and to provide no more space than the colony can effectively patrol. Colonies that have other problems, such as beetle infestations or Varroa mites, are more likely to fall victim to a wax moth infestation. Colonies with too many boxes for the size of the colony also easily become victims.