Johann Martin Fischer arrived in Vienna in1760 to study under the sculptor Anton Tabota. From 1762–1766 he studied at the Vienna Academy under Jakob Schletterer. In 1785 he became a member of the Academy and subsequently assumed the post of professor of sculpture in succession to Franz Anton Zauner as well as the professorship for anatomy. For this appointment he was indebted to Joseph Barth, the famous teacher of ophthalmology and anatomy at the University of Vienna, with whom he shared a lifelong friendship.

Barth was not only one of the most celebrated doctors of his time, but was also regarded as a keen art-lover and collector. Fischer’s appointment to Director of the Academy of Fine Arts in 1815 was the climax of his academic career.

His circle of patrons consisted mainly of public institutions and high-ranking officials. He crafted sculptures for the decoration of public squares and fountains in Vienna. One of his most important patrons was the Princely House of Liechtenstein. As a sculptor he supervised the modifications to the palace in Herrengasse and created the monumental group of the Three Graces for the park in Eisgrub (Lednice).