On July 23, 1850, Miège was appointed the first Vicar Apostolic for the Indian Territory east of the Rocky Mountains, as well as Titular Bishop of Messene, by Pope Pius IX. As required of Jesuit priests, he initially declined the honor, but was then sent a formal mandate from the Holy See. He received his consecration on March 25, 1851 from Archbishop Peter Richard Kenrick, of St. Louis, with Bishops James Oliver Van de Velde, S.J., the Bishop of Chicago, and Jacques-Maurice De Saint Palais serving as co-consecrators, at in St. Louis. Miège departed St. Louis in May 1851, and later arrived among the Potawatomi on the Kansas River. At that time, his vicariate contained five churches, eight priests, and 5,000 Catholics. In 1851 he erected the first Catholic church in Kansas, in Leavenworth, which he also designated as his cathedral. Miège conducted extensive pastoral visitations throughout the wild and remote regions over which his congregation was scattered, visiting the Indian villages, forts, trading posts, and growing towns and celebrating Mass on the rear end of his wagon. He also founded a girls' school for the Osages, placing it under the care of the Sisters of Loretto. In August 1855, he established his episcopal see at the prosperous city of Leavenworth in order to better minister to the growing number of white settlers there. As the number of churches and schools increased, Nebraska was formed into a separate vicariate in 1857 and the Kansas Territory was left under Miège's jurisdiction. He erected an episcopal residence in 1863, and laid the cornerstone of Immaculate Conception Cathedralin September 1864 and dedicated it in December 1868. The cathedral left the vicariate in a debt of $100,000, which he reduced by about half after a trip to South America. He then attended the First Vatican Council from 1869 to 1870. In 1871, desiring a return to the private ranks of the Jesuits, Miège sent his petition to be relieved of his office to the Holy See, which instead gave him Louis Mary Fink, O.S.B., as a coadjutor. His resignation as Vicar Apostolic was later accepted on November 18, 1874. He left 48 priests and 71 churches.
Later life
In January 1874, Miège briefly resumed his duties at St. Louis University. He was then assigned to the Jesuit seminary at Woodstock, Maryland, there serving as a spiritual director. From there he was sent in 1877 to Detroit, Michigan, where he founded Detroit College and served as its first president. Miège returned to Woodstock in 1880, and was stricken with paralysis in 1883. He later died there, aged 68. There are reports that he received a burn while in Woodstock that contributed to his death.