Interesting question because I was also wondering about a museum which only shows the First World War. I have not found something like that, but there are exhibitions in some museums
Bayerisches Armeemuseum (Bavarian Army Museum), Ingolstadt http://www.bayerisches-armeemuseum.de/de/ausstellungen/dauerausstellungen/der-erste-weltkrieg.html
Wehrgeschichtliches Museum (Museum of military history), Rastatt http://www.wgm-rastatt.de/ausstellungen/dauerausstellung/der-erste-weltkrieg/
The seemingly best museum is not in Germany, but in Somme, France: "Historial de la Grande Guerre"
Not in Germany, but within reach: When in school, our class went on a day trip from Germany to Verdun, France.
I highly recommend visiting the Verdun battlefield if you are interested in WWI trench warfare. Thinking about the visit still gives me chills.