Kennedy received a Bachelor of Science degree in chemistry in 1969 from St. Mary's College in South Bend. In 1975, she earned a Ph.D. in biochemistry from Johns Hopkins University in the laboratory of william Lennarz. She moved into the field of neuroscience during postdoctoral fellowships at Harvard Medical School with Edward Kravitz, and then at Yale University with Paul Greengard. In 1981, she moved to Caltech as an assistant professor and was promoted to professor in 1992. She was named Allen and Lenabelle Davis Professor of Biology in 2002.
Her laboratory purified and characterized the synaptic signaling protein Calcium/calmodulin-dependent protein kinase II (CaMKII) in 1983 and showed that it is 1-2% of forebrain protein, is a major constituent of the postsynaptic density, and is regulated by autophosphorylation following activation by synaptic activity.
