The most natural way to say this is " I'm doing my Master's (degree)" You can't say" I'm studying my Master's degree" because the Master's degree is the qualification you get at the end of your period of study , and is not a subject to be studied in itself. You are doing a Master's in ( subject name eg Economics)

I would say 'I am studying for my Master's Degree'. 'For' is used because it is the reason you are studying, it is what you are working towards. However of the two, I would say doing, as Sue says you study the degree, only the subject.