Martin was born prematurely in the village of Ballylongford, County Kerry, Ireland to an English father and an Irish mother - a comfortable, middle-class family. He received his secondary education at Belvedere College in Dublin, and became a Jesuit novice on September 6, 1939 at the age of eighteen. Due to the Second World War and the inherent risks involved with travel during this time, Malachi remained in Ireland and studied at the National University of Ireland where he received a bachelor's degree in Semitic languages and oriental studies while carrying out concurrent study in Assyriology at Trinity College.

Upon completion of his degree in Dublin, Malachi was sent to the Catholic University of Louvain in Belgium to continue his education. During the four year stay in Leuven he completed masters degrees in philosophy and theology and got doctorates in Semitic languages, archeology and Oriental history. On August 15, 1954, the Feast of the Assumption, Martin was ordained a Jesuit priest at the of age thirty-three.

Father Martin started postgraduate studies at both the Hebrew University of Jerusalem and at Oxford University, specializing in intertestamentary studies and knowledge of Jesus Christ and of Hebrew and Arabic manuscripts. He undertook additional study in rational psychology, experimental psychology, physics and anthropology.

Father Martin took part in the research of the Dead Sea Scrolls, and published twenty four articles on Semitic paleography in various journals. He did archeological research and worked extensively on the Byblos syllabary in Byblos, in Tyre, both in Lebanon, and in the Sinai Peninsula. Martin assisted in his first exorcism while staying in Egypt for archeological research. It was upon a Muslim. He published a work in two volumes, The Scribal Character of the Dead Sea Scrolls, in 1958.

Martin travelled publicly and clandestinely to Eastern Europe and Soviet Russia during and after the reign of Pius XII. He carried out sacramental missions and was active in intelligence gathering for the church.

He was summoned to Rome to work at the Holy See as a private secretary for Cardinal Augustin Bea S.J. from 1958 until 1964. This brought him into contact with Pope John XXIII. His years in Rome coincided with the start of the Second Vatican Council (1962–65), all of the sessions he attended and which was to transform the Catholic Church in a way that the initially-liberal Martin began to find distressing. He became friends with Msgr. George Higgins and Fr. John Courtney Murray S.J.

While in Rome, he became a professor at the Pontifical Biblical Institute of the Vatican, where he taught Aramaic, paleography, Hebrew and Sacred Scripture. He during that time also taught theology, part-time, at Loyola University of Chicago's John Felice Rome Center. During that period his living quarters were in the Vatican, outside the papal quarters of John XXIII. He worked for the Orthodox Churches and ancient Oriental Churches division of the Secretariat for Promoting Christian Unity under Cardinal Bea, as a translator. As a result of this, Martin became well acquainted with prominent Jewish leaders, like Rabbi Abraham Heschel, during 1961 and 1962. Martin also accompanied Paul VI in his pilgrimage to the Holy Land in January 1964. Martin resigned his position at the Pontifical Institute in June 1964.

Disillusioned by the reforms taking place among the Jesuits, the Church's largest religious order, Martin requested special dispensation in February 1965. He received a provisional release in May 1965 and a definite release from his vows of poverty and obedience on June 30, 1965, after 25 years as a Jesuit religious and left Rome suddenly in July. He was not released from his vow of chastity and remained an ordained but secular priest. Paul VI gave him a general commission for exercising an apostolate in the media and communications.

After a stay of eight months in Paris, where he worked as a translator, Martin went to Ireland where he stayed with family. During his stay in Ireland he was falsely rumored to have a mental breakdown by local Jesuits. He moved permanently to New York City in 1966, where he first had to work as a dishwasher, a waiter and taxi driver before being able to make his living by writing. He co-founded an antiques firm and was active in communications and media for the rest of his life. The campaign of rumors of a problematic history concerning his mental health and moral behaviour was continued by American Jesuits.

After his arrival in New York, Cardinal Terence Cooke gave him written permission to exercise his secular priestly faculties. The Cardinal advised him to find lodging with a family rather than live alone as he initially did. He moved to the Upper East Side Manhattan home of Kakia Livanos and her family. She was his landlady and provided his rooms, his meals, and the oratory where he said daily Mass.