Wax moths won’t typically kill a healthy hive, but they will not only kill a weaker hive, but they will make a horrible mess of your hive.
Not only will the moths damage your equipment they leave pheromones that will attract new moths after you have killed the old ones, so after you destroy the moths, wipe down your boxes, frames, and equipment with a 10% bleach solution to destroy the smell.
One good way to deal with wax moths, as well as prevent larva from taking hold, is to freeze your frames. Simply putting your comb in the freezer for a week to 10 days during the winter will do a lot to prevent infestation, as well as kill any eggs, larva, or adult moths. Once you have frozen your frames, store them where light can shine in, as this is also a deterrent.
You can also use moth crystals to kill wax moths and their larva. Just make sure you get a product that contains Paradichlorobenzene(PDB). Simply dump the crystals in a large heavy duty garbage bag, and then place the effected frames of comb in the bag, seal and let them fumigate for a month or so. Just remember to let any frames treated this way to be aired out for a month or so, as you don’t want any remaining PDB to kill your bees.
One way or another, the best thing to do is to keep strong hives that can fight off wax moths – so keeping mites and hive beetles well controlled will do a lot to prevent moth infestations.