Shirley Andrews grew up in Melbourne and graduated from the University of Melbourne in 1937 as a biochemist. She worked for the CSIRO as a scientific information officer and from 1953 to 1977 she worked as the biochemist for the Royal Park Mental Hospital. During her time at the hospital she discovered that medicines containing bromureides were contributing to mental dysfunction in patients prescribed with the drug.
In the 1930s Shirley Andrews studied under Edouard Borovansky where she learnt folk dance as well as classical ballet. In the 1940s she worked with Margaret Walker in the Unity Dance Group, a group which used dance to look at social and political issues. Through her dance experience Andrews became interested in Australian traditional dancing. She danced in the musical Reedy River in Melbourne in 1954 and was a founding member of the Victorian Bush Music Club and of the National Folk Festival. Andrews wrote works on dance including Take Your Partners (Victorian Folk Music Club, 1974) and, with Peter Ellis, Two Hundred Dancing Years (Australian Bicentennial Authority, c1988).
Andrews also worked as an activist for Aboriginal rights, including working as secretary for the Council for Aboriginal Rights, and contributed research into Aboriginal status and discrimination.