He was the eldest son of Dr. Martin Tupper (1780–1844), a medical man highly esteemed in his day who came from an old Guernsey family, by his wife Ellin Devis Marris (d. 1847), only child of Robert Marris (1749–1827), a landscape painter (by his wife Frances, daughter of the artist Arthur Devis).
Martin Tupper received his early education at the Charterhouse. In due course of time he was transferred to Christ Church, Oxford where he took his degree of B.A. in 1832, of M.A. in 1835 and of DCL in 1847. At Christ Church, as a member of the Aristotle Class, he was a fellow student of many distinguished men, the Marquess of Dalhousie, the Earl of Elgin, William Ewart Gladstone and Francis Hastings Doyle.