Michael Browne was born in Grangemockler, County Tipperary.
Browne joined the Order of Friars Preachers, commonly known as the Dominicans, in 1903. After studying at Rockwell College, the Dominican convent at the Basilica of San Clemente in Rome, and the University of Fribourg, he was ordained to the priesthood on 21 May 1910.
Browne taught at the Dominican convent in Tallaght, where he was Master of Novices until 1919 when he was appointed professor at the Pontifical University of Saint Thomas Aquinas, Angelicum in Rome.
Browne served as Prior of the convent of St. Clemente from 1925 to 1930.
He was the Angelicum's rector magnificus from 1932 to 1941
Browne was appointed Master of the Sacred Palace from 1951 to 1955.
He became Master General of the Dominicans on 11 April 1955, remaining in that position until his resignation in 1962. Before becoming a bishop, he was created Cardinal-Deacon of S. Paolo alla Regola by Pope John XXIII in the consistory of 19 March 1962. Cardinal Browne was later appointed Titular Archbishop of Idebessus on 5 April 1962. He received his episcopal consecration on the following 19 April from John XXIII, with Cardinals Giuseppe Pizzardo and Benedetto Aloisi Masella serving as co-consecrators, in the Lateran Basilica.
Browne attended the Second Vatican Council from 1962 to 1965. A stern conservative, he was opposed to the reforms of the Council (including religious liberty) and was a friend of Archbishop Marcel Lefebvre. He was one of the cardinal electors who participated in the 1963 papal conclave that selected Pope Paul VI. From 20 January 1971 until his death, Browne served as Cardinal Protodeacon.
He died in Rome, at age 83, and was buried in the priory cemetery in Tallaght, County Dublin, Ireland.
His brother Pádraig de Brún was a notable priest, poet and scholar, and he was an uncle of Máire Mhac an tSaoi, scholar, poet, wife of Irish diplomat, writer and politician Conor Cruise O'Brien, and daughter of his sister, Margaret Browne and her husband, the Irish revolutionary and statesman Seán MacEntee.
The Big Sycamore (1958) is a fictionalised account of the early life of the future Cardinal Browne and his family, fictionalised as 'the Fitzgeralds' (his mother's maiden name was Kate Fitzgerald). It was written (under the pen-name Joseph Brady) by another of his brothers, Monsignor Maurice Browne (1892-1979), parish priest of Ballymore Eustace, County Kildare, and Hollywood, County Wicklow, and the author of plays such as Prelude to Victory (1950), and novels such as In Monavalla (1963) and From a Presbytery Window (1971), as well as the afore-mentioned The Big Sycamore.