Henry Prentiss Armsby (September 21, 1853 – October 19, 1921) was an American agricultural chemist, animal nutritionist, and academic administrator. He served as Vice Principal and Acting Principal of the Storrs Agricultural School (1881–1883), associate director of the Wisconsin Agricultural Experiment Station (1883–1887), and director of the Agricultural Experiment Station (1887–1907) and the Institute of Animal Nutrition (1907–1921) at the Pennsylvania State University.