There area couple of options:
It's quite common to say "I have a masters [degree] in XYZ" for an M.A. or M.S., with the "degree" being optional.
For more specific degrees like an MBA or an MFA (periods optional in those), you would refer to the degree itself, "I have an MBA from Hahvard."
You can also use the degree abbreviation, M.A. or M.S: "I have an M.A. in English from Hogwarts State University."
For more formality, use the full title: "I have a Master of Arts degree from FooBar University."
Note that it's capitalized when you are referring to the specific degree, but not when you are referring to it generically. So, "I have a Master of Arts degree" but "I have a master's degree".