Hazen is a Fellow of the American Association for the Advancement of Science.
The Mineralogical Society of America presented Hazen with the Mineralogical Society of America Award in 1982 and the Distinguished Public Service Medal in 2009. In 2016, he received its highest award, the Roebling Medal. He also served as Distinguished Lecturer and is a Past President of the Society. A mineral that was discovered in Mono Lake was named hazenite in his honor by Hexiong Yang, a former student of his.
In 1986, Hazen received the Ipatieff Prize, which the American Chemical Society awards in recognition of "outstanding chemical experimental work in the field of catalysis or high pressure".
For the book The Music Men, he and his wife Margaret received the Deems Taylor Award from the American Society of Composers, Authors and Publishers in 1989.
For his popular and educational science writing, Hazen received the E.A. Wood Science Writing Award from the American Crystallographic Association in 1998,
In 2012, the State Council of Higher Education for Virginia presented Hazen with its Outstanding Faculty Award.
Hazen has presented numerous named lectures at universities. He gave a Directorate for Biological Sciences Distinguished Lecture at the National Science Foundation in 2007, and was named the Sigma Xi Distinguished Lecturer for 2008–2010.
In 2019, Hazen was named a Fellow of the American Geophysical Union.
In 2021,  Hazen was awarded the Medal of Excellence in Mineralogical Sciences from the International Mineralogical Association.