Heinz Fischer called it "the low point of political culture, which deserves to be universally and roundly condemned."
The cartoon portrays a fat banker with a hooked nose and six-point star buttons on his sleeve gorging himself at the expense of a thin man representing "the people."
Strache denied being anti-Semitic after the cartoon provoked an outcry and demands from the Jewish community that Austria's political establishment condemn the act.
In a speech at the opening of a festival in Linz, Fischer said Strache was playing on the remnants of anti-Semitism in Austria, whose Jewish population was decimated after the annexation of the country by Nazi Germany in 1938.
"To that one can only say in the clearest terms: No way," Fischer said.