Preheat oven to 325°F Grease and flour a 10" Bundt pan.
Stir matcha into yogurt until smooth and lump-free; it will be a vivid, bright green. Sift together flour, baking soda and salt. Set aside.
In a large bowl or stand mixer, cream butter and sugar until light and fluffy. Add eggs, one at a time, beating well to incorporate after each addition. Add vanilla.
Add 1/3 of flour mixture, and beat on low until combined. Add 1/2 of yogurt and beat until combined. Add 1/2 of remaining flour and beat until combined. Add remaining yogurt and beat until combined. Add remaining flour. Beat until just combined, then increase speed to medium-high and beat 2-3 minutes.
Pour batter evenly into prepared pan (it will be very thick). Bake in preheated oven 1 hour or until a cake tester comes out clean.
Cool in pan 10 minutes, then remove from pan and leave on a rack until completely cooled. Dust top with confectioner's sugar.