Henderson was born in southwest Washington, D.C. on November 24, 1883. His father, William Henderson, was a day laborer and his mother Louisa taught him to read at an early age. He often reminisced about Al Jolson having been one of his playmates, as well as how he watched racial segregation grow in Washington after the turn of the century, particularly during the Woodrow Wilson administration. His grandmother Eliza Thomas Henderson had a small store in Washington, but in 1882 (the year before his birth) had moved to Falls Church, Virginia and bought a house at 121 S. Washington Street. Henderson became familiar with that area too, spending summers there and sometimes assisting at that store. The family farm, bought about a decade later, had once been part of Camp Alger. Henderson graduated from Dunbar High School, then the Miner Normal School (now known as University of the District of Columbia) in 1904.