Fungal growth on house plants is caused by improper watering methods, and promoted by inadequate lighting conditions. Powdery mildew is one of the most common fungi known to strike indoor specimens such as your yucca plant. You can effectively treat fungus with good common sense, and some simple everyday products that you already have around the house.
Repot the infected yucca plant. Either sterilize the current container, or buy a new one. Pour about ½ inch of gravel or small pebbles into the bottom of the pot to improve drainage. Use a new package of sterile potting soil.
Place the yucca in a well-ventilated spot with plenty of indirect light. Move it closer to the window for as much direct sun as it can tolerate. Improve air circulation by adding a fan to the sick yucca's room.
Water your yucca just enough to evenly moisten the surface soil. Don't water it again until the surface feels completely dry.
Remove the source of the infection by cutting off the affected leaf as well as all those near or below it. Trim dying leaves from the yucca as soon as you notice them. Always dispose of infected plant material -- don't add it to your compost heap.
Combine equal parts milk and water. Wipe the affected plant's leaves with the solution, which will clean them of dirt, debris and fungus.
Mix a 1/10 solution of mild hand dishwashing soap with water. Wipe the milk residue from the yucca plant's leaves with it. Follow with a clear water wipe, and then gently pat the leaves dry with a soft towel. Repeat steps 5 and 6 every two or three days for a week.