Michael Sheehan was born in Wichita, Kansas to John and Mildred (née Jarboe) Sheehan, and raised in Texarkana, Texas. He attended both St. John's High School Seminary and Assumption Seminary in San Antonio, Texas. He then furthered his studies in Rome at the Pontifical Gregorian University, from where he obtained a Licentiate of Sacred Theology in 1965. Sheehan was ordained to the priesthood in Rome on July 12, 1964.
Upon his return to the United States, he served as parochial vicar at Immaculate Conception Parish in Tyler from 1965 to 1968. Returning to Rome, he earned a doctorate in canon law from the Pontifical Lateran University in 1971. Sheehan served as Assistant General Secretary of the United States Conference of Catholic Bishops/United States Catholic Conference from 1971 to 1976, and as rector of Holy Trinity Seminary in Dallas from 1976 to 1982. In 1982, he was named pastor of Immaculate Conception Parish in Grand Prairie.
On March 25, 1983, Sheehan was appointed the founding Bishop of Lubbock by Pope John Paul II. He received his episcopal consecration on the following June 17 from Archbishop Patrick Flores, with Bishops Leroy Matthiesen and Thomas Tschoepe serving as co-consecrators. He selected as his episcopal motto: "Love One Another Constantly."
Following the resignation of Robert Sanchez, he became Apostolic Administrator of the Archdiocese of Santa Fe on April 6, 1993.
Sheehan was later named the eleventh Archbishop of Santa Fe on August 17, 1993. He was formally installed as Archbishop on September 21 of that year.
Sheehan became Apostolic Administrator of the Diocese of Phoenix on June 18, 2003, after Thomas J. O'Brien resigned in disgrace. He resigned as Apostolic Administrator upon the installation of a fellow Kansan, Thomas J. Olmsted, on the following December 20.
In addition to his native English, he speaks Italian and Spanish.
In August 2009, he decried the attacks by some of his fellow bishops on the University of Notre Dame for having President Barack Obama deliver its commencement speech and receive an honorary degree. Sheehan also said the Catholic community risks isolating itself from the rest of the country and that refusing to talk to a politician or refusing Communion because of a difference on a single issue was counterproductive.
Sheehan has been an outspoken opponent of cohabitation and its effects on marriage. He has released letters to his archdiocese in regards to cohabitation. and its effects on children.