Mix white bean paste and matcha until homogenous. Divide into 6 balls.
Using your hands, stuff each bean paste ball with a strawberry, smoothing the bean paste over the sides.
Set aside while you prepare the mochi.
Add shiratamako, sugar, and water in a bowl. Mix to combine.
Transfer mochi batter to microwave safe bowl (I line my bowl with a damp washcloth) and cover well with plastic wrap, another dish, or other cover. Microwave for 2 minutes and 30 seconds.
Carefully dump cooked mochi onto a surface lightly dusted with katakuriko. Divide into six pieces. While you work with one piece, keep the others covered with a damp cloth so they don't dry out.
Flatten one piece (either with a small rolling pin or your hand), and place a bean paste ball in the center.
Wrap the mochi around the ball, pinching the edges to seal them. Dust in katakuriko to keep from sticking. OPTIONAL: Dust with additional matcha powder on top. Daifuku should be eaten the day they are made.