According to an article in Psychology Today, Their systematic review published in the journal Autism, shows that ... martial arts can all help reduce stereotypic behaviours, improve social and emotional function, and improve cognition and attention.
Training in traditional martial arts requires physical and mental focus. As contrasted with martial arts that that focus exclusively on competition and fighting, traditional here means those practices emphasizing overall skill and character development with movement patterning. Such training is essentially a holistic synergy of mind-body coordination. Habitual practice in martial arts, particularly when structured patterns of attack and defence are repeated, can serve as an excellent tool for physical and mental training.
For those with autism spectrum disorder (ASD), there can be significant sensorimotor issues such as compulsive movement, vocalization, and stereotyped hand and body movements. Major communication issues include impairments in speech development and language. While occupational and physical therapy regimens can be very useful in assisting many with ASD, additional physical activities may be helpful as well.
Emily Bremer and her colleagues at McMaster University and the University of Ontario Institute of Technology in Canada carefully reviewed the available literature on exercise interventions in boys and girls on with ASD from infant to age 16... While there needs to be much more study of these issues, Bremer and colleagues particularly highlight horseback riding and martial arts as activities with strong evidence to produce the greatest results.
E. Paul Zehr (2016)