I will be working on a paid internship in Germany for 2 months. Since, my duration of stay is less than 90 days, I can apply for a schengen visa. However, since I will be paid a stipend, do I need to apply for any other type of visa for the work permit? Or is it included in the schengen visa itself?
I'm assuming you're not an EU citizen.
This page defines internships which require only an ordinary visa for work. Basically, all those which are less than three months and either part of a recognized university course or organized by a German government agency.
If you do not qualify, check this page (in English) which says when you need a visa.