Is reusing part of an internship report self-plagiarism?
As long as you're sure it's appropriate that you are saying the same thing as in the previous assignment (if you're supposed to be achieving something on this internship, shouldn't you be achieving something new?), cite yourself.

It might feel pompous or self-centred at first, but it is the norm in academic texts to cite your own material just as you would anyone else's. Since I imagine your previous report isn't published anywhere, if you can put the previous one online it could be helpful to include the URL so the reader can check the context of the material you're quoting or paraphrasing.

Specific citation styles vary, but they would generally look something like:


  Tully, B. 'Report on my first internship'. Unpublished, available at http://www.internet.com [accessed 1 May 2015].