Paul Arnold Fryxell (2 February 1927, Moline, Illinois – July 11, 2011 Claremont, California was an American botanist.
He attended Moline public schools and later Augustana College, graduating with a B.A. in 1949, and Iowa State University (M.S., 1951, Ph.D., 1955). After employment with the New Mexico Agricultural Experiment Station (1952–1955) and the Wichita State University (Asst. Professor of Botany, 1955–1957), he joined the Agricultural Research Service, USDA, with which agency he spent most of his career as a Research Botanist, located on the Texas A&M University campus. He retired from this position in 1994 and became Adjunct Professor in Integrative Biology at the University of Texas at Austin. He was also an Honorary Curator at the New York Botanical Garden.
His research interests have centered on the taxonomy of the Neotropical Malvaceae, including work on the evolution, biodiversity, and taxonomy of Gossypium, the genus that includes the world's cotton crop. He served as president of the American Society of Plant Taxonomists (1983–1984) and of the Society for Economic Botany (1988–1989), held a Fulbright Scholar Award for study in Argentina (1993), was a Fellow of the American Association for the Advancement of Science and of the Texas Academy of Science, and was a member of the Commission of Flora Neotropica.