James Milton Sheldon Sr. (c. 1880 – July 7, 1965) was an American football player, coach of football and basketball, and college athletics administrator. He served as the head football coach at Indiana University from 1905 to 1913, while also serving as assistant professor of law, compiling a record of 35–26–3. Sheldon was also the head basketball coach at Indiana for one season, in 1906–07, tallying a mark of 9–5. In addition, he served as Indiana's athletic director from 1907 to 1910.

Sheldon died on July 7, 1965, in LaPorte, Indiana.