I'd say talk to both sides about the potential conflict. It is possible that they understand and the class teacher may get out of some classes since you are working an internship that has to deal with your education as well, I know when I was in college I could have. If you think SMing would be something you would be interested in then an internship is a great way to learn some more. I graduated college a year ago and come this October I will be interning at the Goodman Theatre in Chicago, even though I've done a lot of SMing in college (and a little since) its still gonna be a great learning experience interms of me seeing how equity works more up close plus a good line on the resume and networking capabilities.
So yeah just talk to the people about the potential conflict sometimes they will be willing to work with you to make it all work out.