Can I get a masters degree in computer programming with a bachelors in fine arts?

Right now I am attending school to get a Bachelor of Fine Arts Degree in game art and design. While going to school I have found that I very much enjoy coding and think that game programming would be suitable career for me. I feel that if i am going to school for a master's i should have extensive knowledge in coding, but i do not. Basically, I am not sure how the whole masters degree process works. My school does not offer master's degree nor a degree in coding but surrounding schools in my area do. So can I go to school for a masters in programming with a bachelor's in fine arts focusing on game art and design.