Born in Hull, the eldest son of the painter Henry Barlow Carter and Eliza Barlow. He grew up in Scarborough and was educated at Hull Grammar School and St George's Hospital School of Medicine, where he started in 1847. He qualified M.R.C.S., L.S.A. in 1852, and spent a year in Paris following his studies.
On his return to London in 1853 he began studying human and comparative anatomy at the Royal College of Surgeons. During this time he also worked as a demonstrator at St George's Hospital until July 1857. In 1853 he was commissioned to make anatomical drawings for St George's Hospital School of Medicine. He obtained his Bachelor of Medicine at St George's Hospital School of Medicine in 1854, a degree he had initially failed the previous year.
He met Henry Gray at St George's around 1850, and worked with him to illustrate his books, most famously in 1856-1857 Gray's proposed anatomical textbook, which was to be known later as 'Gray's Anatomy'. Gray, however, did not credit Carter for his work on 'On the Structure and Use of the Spleen', 1851, and there were disagreements about acknowledgments as well as pay for Carter's later work.
In 1858 Carter moved to India and joined the Bombay Medical Service, where he became Professor of Anatomy and Physiology at Grant Medical College. He also worked as Assistant-Surgeon in the Jamsetjee Jheejeebhoy Hospital. Between 1863 and 1872 he was Civil Surgeon in Satara. He returned to Europe briefly in 1872 to study leprosy in Norway and elsewhere. Returning to India in 1875, he investigated leprosy in Kathiawar. In 1876 he was put in charge of Goculdas Tejpal Hospital in Bombay, and in 1877 he became Principal of Grant Medical College and Physician of Jamsetjee Jheejeebhoy Hospital.
His publications made important contributions to tropical pathology, particularly in relation to leprosy, mycetoma, and relapsing fever. They include 'The Microscopic Structure and Mode of Formation of Urinary Calculi' (1873), 'On Mycetoma or the Fungus Disease of India' (1874), 'Report on Leprosy and Leper Asylums of Norway' (1874), 'On Leprosy and Elephantiasis' (1874), 'Modern Indian Leprosy' (1876), and 'Spirillum Fever: Synonyms Famine or Relapsing Fever as Seen in Western India' (1882)
He retired with the rank of Deputy Surgeon General in 1888 and became Honorary surgeon to the queen in 1890. He died at Scarborough on 4 May 1897.