Tear out the entire closet ceiling, it can't be saved. Once inside you should be able to see where the leak is located, you may have to turn on the shower if its the drain or shower head. If the leak is active without turning on the shower it is likely a supply line or mixing valve. If you have done this stuff before then go for it, if not call a licensed plumber but you can do the clean up. The mold must be killed, buy a mildewcide with at least 2.4% bleach, I think the chemical name is sodium hydroxide. This is just an ad but it may help
Household Mold: Removing Mold