Frederick Klueg was born on May 1, 1915, in Columbus, Ohio, the second of the five children of Fred and Mary Rose Herbert Klueg. He attended Holy Rosary and St. Aloysius Grammar Schools and Aquinas High School in Columbus, then studied at Providence College, Providence, Rhode Island, from 1933 to 1935.

On August 4, 1935, he received the Dominican habit and the religious name of Eugene at St. Rose Priory, Springfield, Kentucky, and made simple profession there on August 5, 1936. Philosophical and theological studies were taken at the Dominican House of Studies in River Forest, Illinois, from 1936 to 1943. He was ordained in River Forest on June 11, 1942, by Bishop Bernard Shiel of Chicago.

In addition to a B.A. in philosophy (1939) and an M.A. in theology (1943), received at the Dominican House of Studies, Father Klueg obtained a B.S.S.B. in library science (1945) from Rosary College Library School during his first assignment as chaplain and professor at Rosary College, River Forest, Illinois. From 1946 to 1949, he taught philosophy at DePaul

University and religion at St. Xavier College in Chicago, Illinois. During this time he served as librarian at the House of Studies in River Forest as well. In 1949, he was sent to the Angelicum in Rome to continue theological studies and received the S.T.D. in moral theology in 1951. Upon his return to the United States in 1951, Father Klueg was assigned to Saint Rose Priory in Dubuque, Iowa, and served as professor of moral and pastoral theology at Aquinas Institute of Theology and at Mount St. Bernard Seminary, as well as librarian at Aquinas Institute, until 1967, when he accepted a position as professor of theology at the University of Dallas, Irving, Texas, for one year.

Because of ill health, he was advised to go into a ministry that was less strenuous than teaching, and so he served as a hospital chaplain for several years, first as a member of the Catholic Chaplain Corps at the Medical Center in Houston, Texas, from 1968 to 1973; then at Southeastern Louisiana State Hospital in Mandeville, Louisiana, from 1974 to1975. From 1976 to 1980, he served as chaplain to the Dominican Sisters at Rosaryville, Louisiana, as well as acting pastor for the Bedico Mission nearby. During 1981 and 1982, he assisted as a substitute in pastoral supply work in various parishes: St. Bernard, Dallas, Texas; Good Shepherd, Garland, Texas; Holy Rosary, Hahnville, Louisiana; and Saint Louis, King of France in Metairie, Louisiana, where he also served as chaplain at Lakeside Hospital. From 1983 to1984, he was associate pastor at the Cathedral of St. Raphael in Dubuque, Iowa.

Following congestive heart failure in 1984 and an increasingly severe diabetic condition, Father Klueg was moved to the Priory of St. Dominic and St. Thomas in River Forest, where he remained on limited service until his death on April 18, 1988. Following Mass at the Priory on April 20, 1988, he was buried in the Dominican plot at All Saints Cemetery in Des Plaines, Illinois.