There are many picture books about selective mutism written in English. For instance, My Friend Daniel Doesn't Talk, Understanding Katie a Day in the Life of Elisa Shipon Blum Co and Cat's Got Your Tongue?.
Also in Japan, there is at least two picture books about selective mutism.
One of them is Banzai! Nakayama Kun (Hurray! Nakayama). The author is Kyoko Ota. She has written many children's books including: Hito ha Kuma to Tomodachi ni Nareruka? (Can Human Being Become Friends with Bear?), Mama, Daidaidaisuki! (I Love My Mom very very very much!), etc. The illustrator of the picture book is Tadao Miyamoto.
The hero of the book is Nakayama, a first grade boy. He gets into an elementary school, but can't speak in school. One day, he becomes to be able to speak in an empty classroom. And finally, he utters words in front of his classmates in the classroom.
The word "selective mutism" is not found in the book. But the story must be the story of selective mutism. The process of overcoming selective mutism is similar to desensitization.
Unlike fiction, it's not necessarily easy to overcome selective mutism, but this story might give moral support to children with selective mutism.
Index of SM in Japan