I agree with the others that it could be a blood issue such as diabetes or hypo-glycemia.
I also agree that it's just a normal neurological reaction to waking up. My son trembles also when he wakes and it has nothing to do with his blood sugar. The way he reacts to waking is as if he is coming back to reality from a farther place... than us adults. His little body has a hard time dealing with the sensation of waking up. This is totally normal.
And it can even get worst: Some children even tantrum for quite some time as their body wakes up (yelling "No, go away!", kicking, screaming, won't take a bottle to calm down, combative, fighting, smacking at you). Even this is normal. For some it can take up to around 45 minutes to an hour of this screaming and fighting. It's perfectly OK to just check in on these kids every 5 minutes as they lay there tossing, turning, and tantruming until they decide to sip a milk bottle or sippy cup to calm down. It's basically sensory overload to wake up. Sipping can be a calming effect. Milk also has sugar in it, but not as potent as juice.
So, I would agree that you should check with your pediatrician about the blood issues, but also check into the sensory issues as well. If your doc recommends an occupational therapist, I encourage you to follow through. The OC can show you and your son techniques to self sooth and calm the body down, so that he doesn't get afraid of the shaking... and end up as a tantrumer. The techniques are practiced during the therapy session and in a playful way. But, children seem to like them and will use the techniques in many other situations. They seem to figure out pretty quickly what works for them and how to apply their new coping skills.