Martin Kreisig, the first director of the Schumann museum in Zwickau, initiated the establishment of the Schumann Society in the composer’s hometown. Under the Nazis the Society was renamed into ‚German Robert Schumann Society’ and had to set forth a new statute according to the cultural politics of the regime in 1943. After the war Georg Eismann, a Schumann researcher living in Zwickau, asked the almost 700 members to renew their membership. On September 11, 1949 the new Robert Schumann Society Zwickau officially started. But only two years later the association was downgraded and renamed into ‚Robert Schumann Circle‘ — all members from Western Germany were excluded according to the policies of the former GDR. In the meantime the West German members established a new Robert Schumann Society in Frankfurt/Main in 1956; this was an important argument for Eismann to reactivate the existing Zwickau Society, never forgotten by any Schumann enthusiast. However, the regime accepted only the chair of the Society in Frankfurt/Main as a single Western German member. Whereas other associations like the International German Bach Society Leipzig or the Handel Society, founded in Halle/Saale in 1955, had the possibility to operate internationally, the Robert Schumann Society Zwickau was prevented from doing so until 1989. However, the association was given a new statute on June 8, 1990 in order to operate pan-German and international again — and this already four months before the official German reunification in October 1990.

Since its foundation in 1920 the Society has been led by a number of chairmen, among them Lord Mayor Richard Holz (1873-1945), musicologists Prof. Dr. Karl Laux (1896–1978), Dr. Martin Schoppe (1936–1998), Prof. Dr. Helmut Loos and Dr. Gerd Nauhaus as well as Prof. Dieter Zechlin (1926–2012) and Prof. Dietmar Nawroth, both pianists, and conductor Albrecht Hofmann. Since June 2018 Rainer Eichhorn, former Lord Mayor and honorary citizen of Zwickau, acts as chairman. Members of the board include the Lord Mayor being in office and the director of the Robert Schumann House as well as important public figures. The Society maintains good contact with further Schumann institutions in Frankfurt/Main, Düsseldorf, Leipzig, Bonn and Japan. Furthermore Zwickau is a member of the Schumann network based in Bonn.