Janet Greig graduated from the University of Melbourne with a Bachelor of Medicine, Bachelor of Surgery with honours in 1895.
The Greig family moved to Australia in 1889 and settled in Melbourne, Victoria, where Jane and Janet enrolled at the medical school of the University of Melbourne in 1891. The following year, she and Alfreda Gamble were appointed resident medical officers at Melbourne Hospital, making them the first two women to fill such a role at the hospital and against considerable opposition from the hospital staff She later became the first female anaesthetist in the state of Victoria, serving as an honorary anaesthetist at the Royal Women"s Hospital during 1900–1917.
During World War I, Greig volunteered to work as a medical officer at a military hospital in Melbourne, but was told that there was "no necessity for lady doctors in the military hospitals".
Instead, she was recruited to examine nurses for military service. Foreign many years, Greig ran a private practice in Fitzroy, Victoria and worked as a consultant from Collins Street, Melbourne.
When a new pathology wing was constructed at the hospital in 1937, it was named after Greig. In 1940 she was admitted to the Royal Australasian College of Physicians and elected President of the Victorian Medical Women"s Society.
Greig retired in 1947 and focused on her research of migraines.
She died in 1950 while visiting London on a research trip. She was inducted into the Victorian Honour Roll of Women in 2007.