Breitung, the son of John M. Breitung, a Lutheran minister, was born in the city of Schalkau in the Duchy of Saxe-Meiningen, Germany (now in the Sonneberg of Thuringia). He attended the College of Mining in Meiningen, then one of the celebrated schools in Germany for scientific and classical studies. In 1849, after the revolution in Germany, he immigrated to the United States and settled in Kalamazoo County, Michigan. He moved to Detroit in 1851 and became a clerk in a mercantile house. He moved to Marquette and engaged in mercantile pursuits until 1859, when he went to Negaunee. He sold out his mercantile business to engage exclusively in iron-mining operations in 1864, explored the iron range in Marquette and Menominee Counties, locating several profitable mines from 1864 to 1867. He later became interested in gold and silver mining in Colorado.

Breitung was a member of the Michigan State House of Representatives in 1873 and 1874 and a member of the Michigan State Senate in 1877 and 1878. He served as mayor of Negaunee in 1879, 1880, and 1882. He was elected as a Republican to the United States House of Representatives from Michigan's 11th District for the Forty-eighth Congress, serving from March 4, 1883 to March 3, 1885. He declined to be a candidate for renomination in 1884.

Breitung died in Negaunee and is interred in Park Cemetery in Marquette. Breitung's son, Edward N. Breitung, continued his father's successful mining enterprises in the Upper Peninsula of Michigan.

Breitung Township, Minnesota is named after him for his work in developing the Soudan Mine there in the 1880s. Breitung Township, Michigan is also named for him.