Beat the butter and sugar with an electric mixer until pale and smooth. Add the vanilla extract, and eggs one at a time, mixing with each addition.
In a separate bowl, combine the flour, matcha green tea powder, baking soda and salt. Add this to the batter in 2 additions, alternating with the sour cream.
Spoon the batter into a greased and floured bundt pan. Bake at 350F for 45-60 minutes, or until a skewer inserted into the cake comes out clean. Cool completely.