Henry Joseph Haskell was born on March 8, 1874 in Huntington, Ohio, United States. He was the son of Henry Charles Haskell and Margaret Bell Haskell. Members of both families were teachers and ministers, and Haskell's parents went to Bulgaria as missionaries for the Congregational Church in 1862. His father founded the first higher educational institution in the Balkans, which later became the American University at Sofia.
When Haskell was thirteen, he accompanied his parents on their return to Bulgaria; he later said that the three years he spent there aroused his interest in international affairs.