Naumann was ordained to the priesthood on May 24 1975 for the Archdiocese of St. Louis by Cardinal John Carberry. After his ordination, he was assigned as an associate pastor of St. Dominic Savio Parish in Affton, Missouri. Naumann was transferred in 1979 to become associate pastor of Our Lady of Sorrows Parish in St. Louis.
In 1984, Naumann was placed as a part-time curate at Most Blessed Sacrament Parish in St. Louis, while working as coordinator of the anti-abortion committee for the archdiocese. Naumann was sent in 1989 to Ascension Parish in Normandy, Missouri, remaining there for the next five years. He was named vicar general of the archdiocese in 1994.
John Paul II named Naumann as the coadjutor archbishop of the Archdiocese of Kansas City, Kansas, on January 7, 2004, serving under Archbishop James Keleher. When Keleher resigned as archbishop on January 15, 2005, Naumann automatically succeeded him.
Naumann sits on the committees on Pro-Life and on Communications within the United States Conference of Catholic Bishops (USCCB) as well as the Kenrick-Glennon Seminary Board of Trustees and the board of regents for Conception Seminary. He is also chair of the Kansas Catholic Conference.
Naumann was elected chairman of the USCCB Committee on Pro-Life Activities on November 14, 2017, defeating by a narrow margin Cardinal Blase Cupich.[2] Naumann interprets Canon 915 as directing priests to deny communion to Catholic politicians who support abortion rights and euthanasia. He stated that he tried to persuade Kathleen Sebelius, then Governor of Kansas, to change her stand on abortion rights, and after her refusal in doing so, he denied her communion.[3] Naumann's archdiocese later spent $2.45 million in support of an ill-fated proposed amendment to the Kansas constitution to remove its protection of abortion rights, which was defeated by a 59 to 41% margin.[4]
After sexual abuse allegations were made against Bishop John Brungardt of the Diocese of Dodge City in February 2021, the Congregation for the Doctrine of the Faith in Rome directed Naumann to open a canonical preliminary investigation into them.[5] In March 2022, Naumann announced that the investigation had exonerated Brungardt.[6]