Blackburn was born in Hobart, Tasmania on November 26, 1948. She was the daughter of Harold and Marcia Blackburn. She went to Broadford girls school in Launceston, and later Melbourne University High School. She studied biochemistry at the University of Melbourne, completed her PhD at the University of Cambridge, Darwin College, and did postdoctoral work at Yale University. She is now Professor of Biology and Physiology at the University of California, San Francisco. She married John W. Sedat in 1975, and has one child, Ben Sedat. She became a United States citizen in 2003.