That is unusual with ganache under fondant. It did happen to me once, however, on a day with 100% humidity (it was raining and foggy, and pretty warm out as well). A couple of questions: what is the weather where you are? I'm guessing since you mentioned humidity that it is a problem at the moment for you. Perhaps warmth is too. Did the ganache set up so that if you were to touch it gently with your finger, it wouldn't leave a big indent? Ganache does NOT need to be refrigerated, but cakes don't like hot, humid weather, so I suspect the weather is your issue. If your ganache hasn't become firm enough, then you should put the cake in a cooler place -- in the fridge if necessary. Ideally you want to keep the cake under around 75 degrees. Fondant also can be refrigerated; I do it all the time with no problem. Still, if the weather is really humid, a cake will sweat as soon as you take it out of the fridge, so try putting it in a box before placing it in the fridge, and keep it in the box as it warms up. Condensation will form on the box not on your cake. (You can test how humid it really is by taking an egg out of the fridge. If the egg starts to develop big beads of water on it, so will your cake. That's when the box becomes important.)
Sugar is hydrophilic, which means it attracts water, and will grab water molecules out of the air if the humidity is high. You should also consider getting some tylose (also called CMC) from a cake supply store and if it is very humid, mix in a bit of the tylose into your fondant. Tylose tends to make fondant dry out faster, so it will counteract some of the moisture trapping tendencies of the fondant.
Hope that helps.