Qualifications
You only need a high school education, but who says you can't go above and beyond? Getting an associate's degree in industrial maintenance is probably a smart move (source). Two years of school in exchange for a big leg up when you're job-hunting isn't a bad trade-off.
After graduation, you'll take your skills out of the classroom and into...another classroom. Millwrights need to apprentice with a master for about three or four years before they can finally call themselves true millwrights and strike out on their own. Each year of apprenticing involves 144 hours of technical instruction and 2,000 hours of paid on-the-job training.
Yeah, you heard right: paid. Unlike many internships, which pay in experience and networking opportunities, an apprentice millwright gets paid in actual money. Once your apprenticeship is done, you're all set to begin your career.