He was born in Dublin, the second son of Robert Macalister, secretary of the Sunday School Society of Ireland, and his wife. Alexander was educated locally then studied Medicine at Trinity College, Dublin. He qualified at the Irish Royal Colleges in 1861, became M.B. at Trinity Collegeten years later and M.D. in 1876. After acting as demonstrator of anatomy at the Royal College of Surgeons in Ireland, he was appointed professor of zoology, and eight years later professor of anatomy and chirurgery, at Dublin. In 1883 he succeeded Sir George Murray Humphrey in the chair of anatomy at Cambridge, and held this post for thirty-six years. He was a prolific writer. Besides his "Text-book of Human Anatomy" for which he is best known, he was the author of "Introduction to Animal Morphology" and "Morphology of Vertebrate Animals" as well as of numerous papers on animal, morphology, human anatomy and small text-books for students. He was a man of remarkable versatility, being an able mathematician as well as versed in archæology, Egyptology and draughtsmanship. Like his cousin, Sir Donald Macalister, he was a proficient linguist, having knowledge of fourteen languages. Macalister received many honours. In 1881 he was elected a fellow of the Royal Society. He was made hon. LL.D. of the Universities of Edinburgh, Glasgow and McGill and hon. D.Sc. and senator of the University of Dublin. He was Secretary of the Royal Irish Academy and President of the Anatomical Society. His name has been attached to the fovea gastrica and the annulus femoralis s. cruralis.
On 4 November 1910 the body of King Henry VI in its brick vault in St. George's Chapel, Windsor was "investigated", with King George V's consent, by William Henry St John Hope and Canon John Neale Dalton, in the presence of the Dean and Canons, and various other people such as M.R. James, Provost of King's College, Cambridge, and Dr. A. Macalister, Professor of Anatomy at Cambridge. The vault was emptied of rubble, and at the centre was found a small lead chest containing the fragmented bones of "a fairly strong man, aged between 45 and 55", according to Macalister's report, published in The Times on 12 November 1910. The bones had previously been buried in Chertsey Abbey in 1471 until their removal in 1484.