Matthew T. Hendricks was born on February 9, 1845, in Franklin County, Tennessee, to Frederick and Rebecca Hendricks. His father earned a living as a farmer. The family lived in Franklin County, and his father died in the early 1850s. The family moved to Caldwell County, Texas, in the 1850s.
He enlisted in the Confederate army on August 21, 1861, and he mustered in as a private in the 4th Texas Cavalry. He apparently lied about his age, claiming that he was 18 years old. The regiment took part in the New Mexico campaign. He remained in the army until at least December 1862.
He returned to Caldwell County after leaving the army, and he earned a living as a physician. By 1870, he owned $1,800 of real estate and $200 of personal property. In 1874, he helped organize the Caldwell Medical Society. He married Elizabeth Williams on October 26, 1881, but she apparently died soon afterward. He married Guadelupe McDonald on August 11, 1886, but she died on May 7, 1888. Finally, he married Cornelia Hemphill on June 30, 1891. They lived in Lockhart, Texas. He died on November 13, 1915.