Báez was ordained on 15 January 1984 in San Ramón, Alajuela, Costa Rica. He then earned a degree in Sacred Scripture at the Pontifical Biblical Institute. He next served in Guatemala as Rector of the Seminary of the Discalced Carmelite Fathers. Returning to Rome he completed his doctoral studies in Sacred Scripture and Exegesis at the Pontifical Gregorian University. He also took specialized courses at the École Biblique in Jerusalem. Over the next decade he held a variety of academic positions: at the University "Francisco Marroquín" of Guatemala, at the University "Rafael Landívar" in Guatemala, and at the Major Seminary La Asunción in Guatemala, as Professor of Biblical Spirituality at the Pontifical University Urbaniana in Rome. He joined the faculty of the Pontifical Theological Faculty Teresianum in 1994, becoming vice-president of the faculty and editor of the theology journal Teresianum.
On 9 April 2009 Pope Benedict XVI named Báez titular bishop of Zica and auxiliary bishop of Managua. He has served as the Vicar General of the Archdiocese of Managua and is the presiding bishop of the commission on Consecrated life and the presiding bishop of the Seminary of the Episcopal Conference of Nicaragua. Báez and other Catholic leaders in Nicaragua have served as intermediaries between protestors and the administration of President Daniel Ortega since a wave of anti-government protests began in April 2018. He along with Cardinal Leopoldo Brenes Solorzano of Managua, Archbishop Waldemar Sommertag, the Apostolic Nuncio, and other clergy, was injured by pro-government paramilitary forces on 9 July 2018 while attempting to protect St. Sebastian Basilica in Diriamba and free anti-government protesters who had taken refuge inside. The clerical delegation had traveled to Diriamba following the killing of 17 people in the area on 7 and 8 July. Báez was vocal in his criticism of violent repression by the Ortega government. In October 2018, Ortega and his supporters accused Báez of plotting a coup. Government employees reported being forced to sign a letter reiterating the allegations and asking Pope Francis to recall Báez. an investigation by the Spanish newspaperEl Español found that the audiotape produced as evidence against Báez had been doctored. On 4 April, Báez met privately with Pope Francis. On 10 April, Báez announced that Pope Francis had asked him to come to Rome indefinitely. Báez also confirmed that U.S. Ambassador to Nicaragua Laura Farnsworth Dogu told him in 2018 that he was the target of an assassination plot.
