[cites this as an example along a few others. Notably, the [url=Battle of Odžak - Wikipedia]Battle of Odžak](]This answer on Reddit[/url) lasted from May 19–May 25. However, it was fought between Yugoslav Partisans and the forces of the Independent State of Croatia, rather than the Germans or the Italians. So far as I can tell, the Independent State of Croatia was a puppet state of the Axis powers — basically the Croatian version of Vichy France; whether or not that counts as a battle involving the Germans is a grey area.
Also, Wikipedia is similarly unsure about this one; it is cited as "the last World War II battle in Europe.[7][unreliable source?] "