Henry Augustus Middleton Smith (April 30, 1853 – November 23, 1924) was a United States federal judge.
Born in Charleston, South Carolina, Smith received a B.A. from College of Charleston in 1872 and read law to enter the bar in 1874. He was in private practice in Charleston, South Carolina from 1877 to 1911.
On May 25, 1911, Smith was nominated by President William H. Taft to a seat on the United States District Court for the District of South Carolina vacated by William H. Brawley. Smith was confirmed by the United States Senate on June 7, 1911, and received his commission the same day.
On January 1, 1912, the District of South Carolina was subdivided, and Smith was reassigned by operation of law to the newly created Eastern and Western Districts. On March 3, 1915, he was again reassigned, this time to serve only on the Eastern District. Smith assumed senior status on November 23, 1923, serving in that capacity until his death, exactly one year later.