Sigismund I, Prince of Anhalt-Dessau (died Coswig, 19 January 1405), was a German prince of the House of Ascania and ruler of the principality of Anhalt-Zerbst until 1396, when he became the first ruler of the principality of Anhalt-Dessau.
In 1382, after the death of his father, Sigismund inherited the principality of Anhalt-Zerbst jointly with his brothers Albert IV and Waldemar III.
After the death of Waldemar in 1391, Sigismund and Albert became the sole co-rulers.
Five years later, in 1396, both brothers decided to settle upon a formal division of the principality of Anhalt-Zerbst.
Sigismund assumed the title "Lord of Zerbst," but established the town of Dessau as his main residence and capital of his newly created principality of Anhalt-Dessau.