Robert Henri was born Robert Henry Cozad in Miami, Florida to Theresa Gatewood Cozad of Malden, Virginia and John Jackson Cozad, a gambler and real estate developer. Henri had a brother, Johnny, and was a distant cousin of the noted American painter Mary Cassatt. In 1871, Henri's father founded the town of Cozaddale, Ohio. In 1873, the family moved west to Nebraska, where they founded the town of Cozad.
In October 1882, Henri's father became embroiled in a dispute with a rancher, Alfred Pearson, over the right to pasture cattle on land claimed by the family. When the dispute turned physical, Cozad shot Pearson fatally with a pistol. Cozad was eventually cleared of wrongdoing, but the mood of the town turned against him. He fled to Denver, Colorado, and the rest of the family followed shortly. In order to disassociate themselves from the scandal, family members changed their names. The father became known as Richard Henry Lee, and his sons posed as adopted children under the names Frank Southern and Robert Earl Henri (pronounced "hen rye").
In 1883, the family moved to New York City, then to Atlantic City, New Jersey, where the young artist completed his first paintings.