Circulation in the limbs

I often fall asleep on my arm or with my arm under my pillow. When I wake up in the middle of the night my arm is totally numb and sometimes I can't move it (I'm guessing due to lack of blood flow and oxygen to my arm). It's totally involuntary but I'm wondering, is this bad for my arm, my muscle tissue or something of the sort?

Only if it's for an extended period of time. Look up Saturday Night Palsy. However, unless you're drunk, you probably wake up as soon as your limb becomes fully numb, if not before then. I wouldn't worry about it, especially since there's nothing you can really do.