The rare card surfaced at a family history roadshow almost a century after being sent by the future dictator to his comrade Karl Lanzhammer.
Recovering in the German city of Munich in December 1916 after suffering a leg wound in the Battle of the Somme, the then 27-year-old soldier wrote of his intention to "report voluntarily for the field immediately".
Historians say this demonstrates his attachment to his new network of army friends as much as his militaristic zeal.
Dr Thomas Weber, an expert on the period from the University of Aberdeen, said: "What's clear is Hitler desperately wants to return to the front and that's rather unusual, even for soldiers who were generally willing to fight in the war and thought Germany's cause was a just one.
"By 1916, if they were on home leave, they tried to stay as long as they could, while Hitler desperately wants to get back to the front.
"We know from other sources he disliked the sentiment on the home front, where the war was being increasingly criticised, and what he wants is to return to his surrogate family on the front line."
Less unusual is the spelling mistake he makes in the German word "sofort", meaning "immediately", which he spells with two 't's.
"We know from other letters he wrote that there were occasional spelling mistakes," Dr Weber said. "But that was well in line with other soldiers of his background."
The addressee of the card was a member of Hitler's regimental headquarters, supporting the idea he had cut his ties with his pre-war acquaintances.