The following student organizations can help arrange internships:

 

AIESEC arranges international business internships. All concentrators may apply.

Contact:  aiesec.info@umich.edu or www.aiesecmichigan.org/

IAESTE arranges internships for international positions in primarily scientific and technical jobs.

Contact:  iaeste.eb@umich.edu or www.umich.edu/~iaeste/

The U M International Center (IC)  Overseas Opportunities Office  has information on working, traveling, volunteering and study abroad opportunities.  Language departments also have information on study abroad and work abroad opportunities.
Office of International Programs (OIP) has study abroad programs that feature internships. 
See:  Study Abroad Internship Programs

For other international internships,

Also, see University of Michigan-Dearborn: Ottawa Political Internship Program - Ottawa, Canada