Itzig was born in Berlin. His family was mercantile; His wife Miriam's ancestors included Rabbi Moses Isserles of Cracow and Joseph ben Mordechai Gershon. Itzig was a banker in partnership with Feitel (Efraim) Heine. Together they owned factories for oil and lead. During the Seven Years' War he assisted Frederick the Great. Following the war he was appointed in 1756 Master of the Mint, and was made the Prussian court banker by Frederick's successor, Frederick William II in 1797.
Itzig was one of the very few Jews in Prussia to receive full citizenship privileges, as a "Useful Jew". He became extraordinarily wealthy as a consequence.
Together with his son in law David Friedlander, Itzig was appointed to lead a committee which was to discuss ways to improve the Jewish civil and social standing in Prussia, which led to the removal of many restrictions. He funded early members of the Haskalah secular movement, including Rabbi Israel of Zamosch (Moses Mendelsohn's teacher), Samuel Rominow (an Italian Jewish artist) and Isaac Satanow.
In 1761 he began planning a school for poor Jewish boys in Berlin, and in 1778 his son together with Daniel Friedlander opened the first "free school" (Freischule) called "Hinuch Neorim", Hebrew for 'Teaching the Young Ones'. The school and adjacent printing house later became one of the main institutions of the Haskalah movement. At the same time he founded and funded a Yeshiva and brought Rabbi Hirschel Levin and Rabbi Joseph ben Meir Teomim to Berlin to teach there.
Itzig was official head ('Oberältester') of the Jewish community in Berlin from 1764 until his death in 1799.
Many of Itzig's thirteen children by his wife Miriam Wulff who lived to adulthood became influential in German Jewish society. Two of his granddaughters married two of Moses Mendelssohn's sons. One of them was Lea (née Solomon), mother of Felix Mendelssohn and Fanny Hensel, a pianist and composer. By her, Lea was grandmother of mathematician Kurt Hensel.
- Conway, David (2012). Jewry in Music: Entry to the Profession from the Enlightentment to Richard Wagner. Cambridge: Cambridge University Press.