Pressure on the nerves as they leave the neck and travel down the arm can cause this to happen. Sometimes this kind of numbness occurs because you have slept in the same position for too long. It can also happen if your bed and pillow do not give you enough support for your head and neck.
The first place to start is with a check of your mattress, which should be firm. It should not sag or be so hard that it doesn’t have any give to it. Your pillow can be made with feathers, foam, or other manmade materials, but it should be firm enough to support your head and neck in a straight line. There are pillows made just for this purpose. They can be purchased in many retail bedding stores, a medical supply store, or from a local chiropractor or physical therapist.