You know that most Master’s programs are specific about what background they require, and that they decide whether to offer you a place, right?
For example, here are the application requirements for a Masters in Art History at Hunter College (part of the City University of New York system): http://www.hunter.cuny.edu/graduate-programs/arts/art-history/ah-graduate-program.html#program
That’s a little more than studying on your own. You could do it by taking Art History classes at a community college (for example: https://www.bmcc.cuny.edu/academics/departments/music-and-art/art-foundations-art-history/). It would be a bit of a gamble, as there is no guarantee that that would be enough to get you admitted to that Masters program, but it is a pathway.
You also need to research the specific Masters programs- they focus on different things.