How do you politely tell your friend that he/she is not invited in your wedding when they ask?

I would be honest and upfront about it that you are keeping it to a certain group. As much as people want to be involved in weddings and celebrations, I happen to believe that it should be as private as the couple wants it to be. This friend should respect that he simply didn't make the cut. If he wants to celebrate with you, there are many ways to demonstrate his support outside of attending the wedding.