People will advise you to use bleach or ammonia or boric acid. All are somewhat effective, with the boric acid having a continuing mold suppressive quality. However, all of these only get the mold on the surface. The fungal roots deeper in the wood or drywall are not killed. If the area stays dry the mold may not become problematic, but it's still there.

Look for a true mold killer such as MoldSTAT Plus, or Concrobium Mold Control. These won't necessarily remove all mold stains, but they do kill the mold. Most often these products are concentrates that are mixed with water and applied via a pump-up sprayer, but there are some ready-to-use mixtures. MoldSTAT Plus is sold via Walmart, and Concrobium is sold through both Lowes and Home Depot. However, they may not be kept in stock; a lot of things are available only through their online store.