She attended Croydon High School. She graduated from Girton College, Cambridge, one of the first woman to be admitted to the Honours Degree Examination at the University of Cambridge in 1882. After graduating she studied medicine at the London School of Medicine for Women and in Edinburgh, where she qualified as a doctor of medicine in 1891.
She founded the Christian Medical College Ludhiana, the first medical training facility for women in Asia, and served as principal of the college for half a century. Brown was a pioneer in the instruction of Indian female doctors and midwives with modern western methods. Her older sister was a missionary, which led to Brown developing an interest in medicine and missionary work.
The Baptist Missionary Society sent Brown to Bombay, where she arrived on 9 November 1891.
Brown was shocked by medical conditions in India and felt a need to educate women, particularly midwives. Trained Indian women doctors or nurses were almost unknown, and throughout the peninsula only one or two women"s hospitals existed."
After two years with various missions, Brown set out on her own.
In January 1894, a woman in Bristol donated ₤50 (£5,085 today) to help Brown rent an old schoolhouse in Ludhiana, Punjab. She organised a Christian medical training center for women, the North India School of Medicine for Christian Women, starting with four students and four faculty.
The medical school, the first for women in India, grew into a full college with medical, nursing and pharmacy schools, and a hospital with 200 beds.
The college was supported by significant grants from the Punjab governments, as well as women"s auxiliaries in London, Edinburgh, Glasgow as as well as Australia, Canada, the United States and New Zealand. The school was renamed Christian Medical College Ludhiana in 1911, though it had opened its doors to non-Christians since 1909. During the partition of British India in 1947, Punjab was split between India and Pakistan, resulting in massacres of thousands in Ludhiana.
Despite the violence, the college and hospital remained safe from attack.
The hospital became an emergency centre for the seriously injured. By November 1951, on the 50th anniversary of Brown"s arrival in India, the college had graduated 411 doctors, 143 nurses, 168 pharmacy dispensers and more than 1,000 midwives.
Brown retired as principal in 1952 and moved to Kashmir. In the 1932 New Year Honours, Brown was made a Dame Commander of the Order of the British Empire.
Brown died 6 December 1956 in Srinagar, India, aged 92.