Dodd was born in Wrexham, Denbighshire. He was brother of the historian A. H. Dodd. He studied classics at University College, Oxford, from 1902. After graduating in 1906 he spent a year in Berlin, where he was influenced by Adolf Harnack.
He was a Congregationalist minister for three years in Warwick, after being ordained in 1912, before going into academia. From 1915 he was Yates Lecturer in New Testament at Oxford. He became Rylands Professor of Biblical Criticism and Exegesis at the Victoria University of Manchester in 1930. He was Professor of Divinity at the University of Cambridge from 1935, becoming emeritus in 1949. His students from Cambridge include David Daube and W. D. Davies. The three together, each through his own work, ushered in changes in New Testament studies that led to the New Perspective on Paul and the scholarship of Davies's student, E. P. Sanders.
He directed the work of the New English Bible translators, from 1950.
Dodd died in Goring-on-Thames, Ixfordshire, England. His daughter Rachel married the Old Testament scholar Eric William Heaton in 1951.