Preheat the oven to 350°F. Grease an 8 ½-inch x 4 ½-inch loaf pan, or line it with parchment paper. Set aside.
In a large mixing bowl, combine the self-rising flour with the granulated sugar. Set aside.
Add the yogurt, oil, eggs and vanilla extract to a smaller mixing bowl. Mix until well combined.
Pour the wet ingredients into the bowl with the flour mixture and mix until just combined. The mixture will be very thick. Fold in the chopped apple and grated zucchini.
Spoon the batter into the prepared baking tin. Bake for 50 minutes, or until lightly golden and cooked through. Allow to cool in the tin for 10 minutes, before removing from tin and transferring to a cooling rack to cool completely.
To make the cream cheese glaze, add the powdered sugar, cream cheese, milk and vanilla extract to a small mixing bowl. Mix until smooth and well combined.
Drizzle or spread over the cooled apple zucchini bread.