Danzig is a German-language surname. Notable people with the surname include:
Avraham Danzig (1748–1820), rabbi, author of works on Jewish law
Glenn Danzig (born 1955), American rock vocalist, songwriter, and publisher
Richard Danzig (born 1944), American lawyer and former Secretary of the Navy
Mac Danzig (born 1980), American professional mixed martial arts practitioner
George Dantzig (born 1914), American mathematical scientist