Harry Francis Craft (April 19, 1915 – August 3, 1995) was an American Major League Baseball player and manager. Born in Ellisville, Mississippi, he was a center fielder for the Cincinnati Reds from 1937 to 1942. Craft attended Mississippi College, threw and batted right-handed, stood 6 feet 1 inch (1.85 m) tall and weighed 185 pounds (84 kg).

From 1962 through September 18, 1964, Craft was the first manager in Houston's Major League history as skipper of the expansion Houston Colt .45s, later the Astros. Earlier, he managed the Kansas City Athletics (August 6, 1957–1959) and he was the "head coach" of the Chicago Cubs (April 26–May 10 and June 2–4, 1961).