He graduated at Pembroke College, Cambridge in 1661, and ten years later took the degree of M.D. at Leiden University, his thesis being Disputatio medico-physica de liquore nervoso.
Nehemiah Grew began observations on the anatomy of plants in 1664, and in 1670 his essay, The Anatomy of Vegetables begun, was communicated to the Royal Society by Bishop Wilkins, on whose recommendation he was in the following year elected a fellow. In 1672, when the essay was published, he settled in London, and soon acquired an extensive practice as a physician. In 1673 he published his Idea of a Phytological History, which consisted of papers he had communicated to the Royal Society in the preceding year, and in 1677 he succeeded Henry Oldenburg as secretary of the society.
Nehemiah Grew edited the Philosophical Transactions in 1678-1679, and in 1681 he published by request a descriptive catalogue of the rarities preserved at Gresham College, with which were printed some papers he had read to the Royal Society on the Comparative Anatomy of Stomachs and Guts.
In 1682 appeared his great work on the Anatomy of Plants, which also was largely a collection of previous publications
Among his other publications were Seawater made Fresh (1684), the Nature and Use of the Salt contained in Epsom and such other Waters (1697), which was a rendering of his Tractatus de salis (1693), and Cosmologia Sacra (1701).