Most likely, you are seeing a form of repetitive movement that is common among children diagnosed with autism. I recommend seeking some advice from your son's ABA therapist, if he is still working with one. A common intervention for repetive movements involves interrupting those movements as soon as they begin to occur. For example, a light touch to the shoulder might be enough to interrupt the shaking without distracting your son from his reading. Given that your son is in 4th grade, it may be useful to work with his school on a self-monitoring program that would teach your son to recognize when he is shaking his head and to reward him for reading without head shaking. I would also mention this concern to your son's pediatrician so that he can assess your child in person to rule out other issues.
I am not a professional, I am a parent of a child with an ASD.
A possibility you might like to rule out is Irlen Syndrome. Alot of children/adults with autism and dyslexia have this. It is a visual perceptual problem which is easily helped by wearing tinted glasses or by using tinted overlays for written work.
If you google Irlen Syndrome, it should give you alot of information about it. It is a recognised medical condition.