Your shoulder may be tight due to the way you slept. Many days of the week I wake up and my shoulders are also tight. The reasoning for this related to how I sleep which is most often on my left side. By sleeping on my left side my body is slightly hunched over and this was not how my body was designed. Our bodies are not designed to stay in certain positions for over extended periods of time.
Think of it this way, when you are at work, and if you have a desk job similar to most Americans, do you find that one area of your body is tight at the end of the day? It might be your hips, it might be your back, everyone is different but we all experience stiffness from prolonged periods of time spent in one position. Most likely your reasoning for tightness is due to the way you are sleeping. Be sure to replace your pillow as necessary and try to sleep on your back. If you are able to complete this then it may prevent shoulder tightness. If you are already doing everything listed then please reply with some more details so I can try and assist you.