If you're in the US it is not illegal to work in an unpaid internship if you aren't a student.
Internships do have a few considerations that employers need to meet.
Midlife or second career internships have been becoming much more common over the years with a good deal of people starting up in second careers, say after an initial retirement.
While I personally see most unpaid internships as taking advantage of someone, if that's what you want to do it just takes work.
Contact recruitment ads targeted at student interns and apply anyways, get your resume in there and when the subject of school comes up explain where you're at, what you want to come away with, and what you can bring to the table. Hiring ads are often not carved in stone.
Shop around local businesses in the industry and offer your services free of charge for a few months with an interest in padding your resume and getting some real life experience. There's a lot of struggling businesses out there that would probably be willing to get a free inexperienced hand in exchange of teaching them some of the trade.
Just put yourself out there, go get rejected a whole bunch, eventually someone will bite.
That being said, understand what you're looking for. You aren't just free labor, if you aren't getting tangibly compensated you aren't an employee. Make sure you're not being used as strictly an employee. You're there to learn, first and foremost, so don't let yourself be taken advantage of, if it stinks walk away.
In my opinion, with a masters degree in computer science and not knowing how to program, you're probably going to have a rough go of it. If it was me, I would start programming my ass off and shoot off as many offers to be an intern as I could. If you don't think you can genuinely learn to program, learn how to script and see if you can get some kind of admin job. That degree will for sure open doors, whether you get to stay in the house is a totally different matter.