After acting as house surgeon to the Maternity Hospital of Edinburgh, Balfour in 1846 went to Vienna, where he studied under Joseph Škoda, Carl Ludwig Sigmund, and Wilhelm Fleischmann the homeopath.
Balfour specialised in diseases of the heart and circulation, a leading figure of his time in the area with Sir William Tennant Gairdner in Glasgow, and Charles Hilton Fagge in London.