Yes. Non-EU/EEA students are allowed to work in Germany alongside their
studies, for 120 full days or 240 half days per year. If you take an internship during your semester break, this is regarded as normal work, even if it’s unpaid. This means that every day of your internship is subtracted from your 120-day credit balance. However, mandatory internships which are required for your course do not count towards your limit. However, non-EU students are not permitted to work in a self-employed or freelance capacity.
Students in Germany can earn up to €450 (~US$491) per month tax-free. If you earn more than this, you will receive an income tax number and have automatic tax deductions from your salary.