This is more commonly known as bracket fungi and usually attacks weak or dead trees. Often it is not threat, but requires a professional arborist to diagnose and treat.
With an anti-fungal spray. They sell them at most do it yourself stores, nurseries and super centers. Check the label to make sure it wont ruin what you are spraying.
A number of common kitchen ingredients are anti-fungal, and can be put in the watering can or in the mister to help kill off the fungus. Cinnamon is very potent, and smells good. Cayenne pepper also works and is readily available.
The best is to wash the shelf with a hot water/bleach mixture. That will kill what is there. To control its return, you need to find out why it is damp which allows the fungus to develop. Hardware stores sell products that remove the moisture from small areas.
This is wood rotting fungus. If this fungus increased, tree dies with in short period, to avoid it mix shrubs insecticides in water and pour in the base tree soil
Shelf fungus can be very annoying and difficult to get rid of once it takes hold. The first thing you need to do is to make sure it is indeed a shelf fungus and not just a fungus growing on your shelf. Once you have verified, get any anti-fungal product sold in a outdoor store.