Duveneck was born in Covington, Kentucky, the son of a German immigrant Bernard Decker. Decker died when Frank was only a year old and his widow remarried Joseph Duveneck. By the age of fifteen Frank had begun the study of art under the tutelage of a local painter, Johann Schmitt and had been apprenticed to a German firm of church decorators. While having grown up in Covington, Duveneck was a part of the German community in Cincinnati, Ohio. However, due to his Catholic beliefs and German heritage, he was an outsider as far as the artistic community of Cincinnati was concerned. In 1869 he went abroad to study with Wilhelm von Diez and Wilhelm Leibl at the Royal Academy of Münich, where he learned a dark, realistic and direct style of painting. He subsequently became one of the young American painters — others were William Merritt Chase, John Henry Twachtman, and Walter Shirlaw — who in the 1870s overturned the traditions of the Hudson River School and started a new art movement characterized by a greater freedom of paint application.
His work, at first ignored, when shown in Boston and elsewhere about 1875, attracted great attention, and many pupils flocked to him in Germany and Italy, where he made long visits. Henry James called him "the unsuspected genius" and at the age of 27 he was a celebrated artist. In 1878 Duveneck opened a school in Munich, and in the village of Polling in Bavaria. His students, known as the "Duveneck Boys", included Twachtman, Otto Bacher, Julius Rolshoven, and Herman Wessel. In 1886 he married one of his students who was much admired by Henry James, Boston-born Elizabeth Boott. They lived in Bellosguardo for two years where she produced a son. She died later in Paris of pneumonia. Duveneck was devastated. After returning from Italy to America, he gave some attention to sculpture, and modelled a fine monument to his wife, now in the English cemetery in Florence. Despite this activity, Elizabeth's death marked a slowing in his productivity - a wealthy man, he chose to lead a life of relative obscurity. He lived in Covington until his death in 1919 and taught at the Art Academy of Cincinnati, where some pupils of note were Edward Charles Volkert and Russel Wright.
In later years, he often spent summers in Gloucester, Massachusetts.
Among his most famous paintings are Lady with Fan (1873) and The Whistling Boy (1872), both of which reveal Duveneck's debt to the dark palette and slashing brushwork of Frans Hals. His work can be seen at the Metropolitan Museum of Art in New York City, the National Gallery of Art in Washington, DC, the Cincinnati Art Museum, the Richmond Art Museum and the Kenton County Library in Covington, Ky.
Duveneck is buried at Old Mother of God Cemetery, Madison Avenue and 26th Street, Covington, Kenton County.