Rietz studied the cello under Bernhard Romberg. At 16, he joined the orchestra of Berlin's Königstädter Theater, for which he wrote the music to Karl Eduard von Holtei's play Lorbeerbaum und Bettelstab. In 1834, he was appointed assistant conductor at the Düsseldorf Opera under Mendelssohn, whom he succeeded the following year. He moved in 1847 to Leipzig, where he served as kapellmeister and conductor of the Singakademie. During 1848, a year after Mendelssohn's death, Rietz took over Mendelssohn's former role as conductor of the Gewandhaus concerts in the same city, and as teacher of composition at the conservatoire there. He was called to Dresden in 1860 to succeed Carl Gottlieb Reissiger as court kapellmeister. Here he spent the rest of his life, frequently appearing as an opera conductor, and also undertaking the direction of the royal conservatoire.
In terms of his own composing, Rietz belonged to the classically inclined school (Mendelssohn's output, as might be expected, had a big influence upon him) and he was strongly opposed to the musical radicalism of Liszt and Wagner. Among his works are the operas, three symphonies, several overtures to plays, flute sonatas, violin sonatas, motets, masses, psalms, and a quantity of other church music.
The Louisville Orchestra First Edition series contained, besides many works mostly by modern composers (usually American), Rietz' Concert Overture, opus 7 (coupled with the second symphony of Max Bruch), and recorded around 1970. This may have been the same concert overture commissioned by the Lower Rhenish Music Festival to commemorate an anniversary .