1918, "date set for the beginning of a military operation," with D as an abbreviation of day; compare H-hour, also from the same military order of Sept. 7, 1918:
The First Army will attack at H-Hour on D-Day with the object of forcing the evacuation of the St. Mihiel salient. [Field Order No. 8, First Army, A.E.F.]
"They designate the day and hour of the operation when the day and hour have not yet been determined, or where secrecy is essential" [U.S. Army Center of Military History Web site]. Now almost exclusively of June 6, 1944.