According to Chron.com, internships, even short ones and unpaid ones, are a form of employment. They provide essential experience and should be included on your resume.

Is interning a work?

An internship is a short-term work experience offered by companies and other organizations for people—usually students, but not always—to get some entry-level exposure to a particular industry or field. It is as much of a learning experience as it is work.

Are you employed as an intern?

The FLSA requires “for-profit” employers to pay employees for their work. Interns, however, may not be classified “employees” under the FLSA—in which case the interns are not entitled to compensation for their work. ... Any promise of compensation, express or implied, suggests that the intern is an employee—and vice versa.