The doughboys of Battery E, 11th Field Artillery carefully loaded the 95-pound shell into Calamity Jane, the name of their favorite 155mm artillery piece. With the round in place, the men locked it into the breech and prepared to pull the lanyard. An officer, looking at his watch, stepped forward. Raising his hand, he kept his eye on his watch, waiting for the second hand to reach twelve. When it did he dropped his hand. A soldier yanked the lanyard. Calamity Jane was fired one at 1100 hrs, 11 November 1918. World War I was over.
There is no explanation why the 11th was chosen, but it is possible some enterprising officer in the American high command noticed the succession of elevens in the cease-fire order and picked the 11th to play along with the consistency.
Source: Army History, 20 January 2015