Born in Belzig, Reissiger attended the Thomasschule zu Leipzig and was the pupil of Johann Gottfried Schicht and Peter von Winter.
Reissiger continued his musical studies in France and Italy in 1824, under the sponsorship of the Prussian Ministry of Cultural Affairs.
Reissiger left behind an extensive oeuvre that was distinguished above all by his vocal music, which included nine operas, one oratorio, nine Latin masses and another four in German, as well as sixty lieder.
Reissiger's most successful compositions were the operas Didone, Der Ahnenschatz, Libella, Die Felsenmühle, and Adèle de Foix, and the melodrama Yelva.
His great masses, composed for Catholic services at Court, carry rich melodies and warm feeling.