My grandparents owned a store in Bremen, Germany in 1914 when World
War I broke out.  We have been told that Grandpa Jan Broers, a citizen
of the Netherlands, was arrested and placed in an internment camp
somewhere in Germany.  Where was he interned, when was he arrested,
and when was he released?

A first port of call, even if they might not be able to help you
directly, is the Red Cross, which maintains a world-wide network of
tracing services in relation to people who have lost contact with
their families during conflicts. I say the might not be able to help
for the simple reason that they give priority to finding people who
are - likely - still alive, and if your grandfather owned a store in
Bremen in 1914 he must have been reasonably adult so without being to
pessimistic about things I would guess he is no longer with us.

Contact the Red Cross in the country where you live.

A second possibility, depending on the size of your family and how
much you know about it would be to consult some of the genealogical
websites and services - not because you don't know about him but some
one else may have listed him as a descendant of somebody else, and
have information available for that reason.

Best of luck!

As suggested by erkowit-ga you could ask a genealogical society. I
would recommend "Die Maus" Gesellschaft für Familienforschung Bremen

http://www.dbv-bremen.de/html/bibfu/diemaus.html
and
http://www.genealogienetz.de/vereine/maus/

You could also ask the "Staatsarchiv Bremen"
http://www.bremen.de/info/staatsarchiv/kontakt.htm

An overview of the holdings of the Staatsarchiv is searchable online:
http://www.bremen.de/info/staatsarchiv/bestand/ubersich/starter.htm

However, these webpages are written in German.

The Netherlands Institute for War Documentation (NIOD) was founded as 
"the centre in the Netherlands for information and research on the
Netherlands (including the Dutch East Indies) during the Second World
War."

However, they could provide you with the information you are looking for as
"a few years ago the scope of the Institute was widened and its
research field was formulated as the history of the two world wars in
their contemporary historical context, including their long-term
effects on society."

http://www.niod.nl./content/en/general.asp

http://www.niod.nl./contact/start_en.asp