"Moi" is a pronoun and so it's like a noun, it can stand by itself. "Ma" is traditionally an adjective in French, but unlike the "adjectif qualificatif" that can stand on its own when used with certain verbs (être, paraitre, devenir, sembler, …), "ma" needs the support of a noun, that is, as it is probably more judiciously classified in English grammar, "ma" is a determiner; there are people in France nowadays that think so too. So, you always need a noun after "ma". You can say that "ma" refers to something or someone; instead, we say rather that it determines someone or something and here it determines someone, the person in possession of the towel.
Therefore you can't say "La seviette est ma.". If you want to formulate the idea of possession with a determiner instead of a pronoun, in French you say this.
There is another pronoun that can be used in another construction that says about the same thing, but it is not heard as often.
- Cette serviette est la mienne.
Those pronouns are made up of two words, an article and a pronoun (le mien, la mienne, le tien, le sien, …) (réf.).