Archbishop Sheehan was born in Wichita, Kansas. He attended Catholic Schools in Texarkana, Texas and St. John’s High School in San Antonio, Texas. He studied for the priesthood at Saint John's Seminary and Assumption Seminary in San Antonio, Texas and completed his priestly formation at the North American College in Rome, Italy. He did his Theological Studies at the Gregorian University where he received his S.T.L. Degree in 1965. In 1968, he returned to Rome for studies in Canon Law and received his doctorate from the Lateran University in Rome in 1971.

He was ordained a priest, to the Diocese of Dallas-Fort Worth, in Rome on July 12, 1964. He was appointed associate pastor for Immaculate Conception Parish, which is now the Cathedral Parish in Tyler, Texas. He served there from 1965 to 1968. From 1971 to 1976, he served as Assistant General Secretary for the National Conference for Catholic Bishops and the United States Catholic Conference in Washington, D.C. In 1976, he was appointed rector of Holy Trinity Seminary in Dallas and served there until 1982 when he was named Pastor of Immaculate Conception Parish in Grand Prairie, Texas. On June 17, 1983, Pope John Paul II established the Diocese of Lubbock and named Monsignor Michael Jarboe Sheehan as its first Bishop. He served as Bishop of Lubbock until April 6, 1993 when he was appointed Apostolic Administrator for the historic Archdiocese of Santa Fe. He was appointed the eleventh Archbishop of Santa Fe on August 17, 1993 and installed at the Convention Center in Albuquerque on September 21, 1993 by Archbishop Agostino Cacciavillan, Apostolic Pro-Nuncio to the United States. Archbishop Sheehan was appointed Apostolic Administrator for the Diocese of Phoenix on June 17, 2003 - the same date he celebrated his 20th Episcopal Anniversary serving 10 years as Bishop of Lubbock and 10 years as Archbishop of Santa Fe. This appointment ended on December 20, 2003 when a permanent Bishop was appointed to Phoenix. He finished his term as e Secretary of the Executive Committee for the USCCB and Chair of the USCCB Plans and Priorities Committee in November 2006. He currently serves on the Boards of Josephinum Seminary, Catholic Extension Society and Catholic Mutual.

He has served on various USCCB committees: Administrative, Liturgy, Evangelization, Communications, Hispanic Affairs, Priestly Life and Ministry to mention a few. He has also served on a variety of Board of Directors: Holy Trinity Seminary in Dallas, Mexican American Cultural Center, United Way Program, and RENEW International among others. He served as Episcopal Moderator for the National Catholic Young Adult Ministry Association from May 2002 until September 2006.