As a junior in college, Delaney Dunne took an internship for class credit and $10 an hour at co-working company TekMountain in Wilmington, N.C.

On graduation day this year, she received a letter from TekMountain’s parent asking about her employment status and reminding her she had signed a noncompete agreement with TekMountain in November 2017 that restricted her employment options.

“I burst into tears hours before I was set to graduate from college,” Ms. Dunne, 22, said. “That noncompete (agreement) that I signed when I was 20 years old was still haunting me.”

Internships have long been an opportunity for inexperienced workers to try out different industries and build valuable contacts. For companies, it is a way to attract future talent.

But increasingly interns are being asked to sign noncompete, nondisclosure and forced arbitration agreements, restrictions once reserved for higher-ranking employees.