Henry Geiger was born in Illinois in August 1871, the son of Charles A. Geiger (d. 1926), a German immigrant, and Mary Katherine Weinsheimer (b. 1850). Mary and Charles married on October 25, 1870, and had eight children: Henry, Emma, Wallace, May, Edith, Earl, Wilbur, and Herbert. The family lived in Galena, Illinois.
Henry Geiger began courting Mildred Palmer before 1890, and they married between 1896 and 1898. He served as captain for Company M of the 6th Regiment, Illinois National Guard, and he traveled with them to Puerto Rico during the Spanish-American War. During World War I, he was a musket instructor at Camp Cody, New Mexico; a member of Company C of the 125th Machine Gun Battalion; and a member of the 34th Division's 109th Ammunition Train in France. In his civilian life, Geiger worked as a bricklayer in Galena, and he later owned a construction contracting business in Sheldon, Iowa, where he lived with his wife and children.