Abelson received many distinguished awards, including the National Medal of Science in 1987, the National Science Foundations Distinguished Achievement Award, the American Medical Associations Scientific Achievement Award, the Navy Distinguished Civilian Service Medal and the Waldo E. Smith Medal in 1988. In 1992 he was awarded the Public Welfare Medal, the National Academy of Sciences's highest honor. He was elected a fellow of the American Physical Society in 1949 and the American Academy of Arts and Sciences in 1958. He was elected to the American Philosophical Society in 1961.
The mineral abelsonite is named after Abelson in recognition of his contribution to organic geochemistry.
The Philip and Neva Abelson Hall at Washington State University was named in his honor.
The AAAS Philip Hauge Abelson Prize is named after Philip Abelson.