The building was erected in 1906 at the direction of the Kherson City Duma. The project was developed by the Russian architect of Jewish descent Adolf Boruchovich Minkhus, who lived from 1870 to 1948.

Before the establishment of communist power, the building housed city administration bodies, judicial institutions, and a bank.

In the 1920s, the building was transformed into an art museum, where the main part of the collection consisted of works of Russian and Western European painting. During the Nazi occupation, a significant portion of the exhibits was taken to Germany and Romania. In 1981, the museum was named after the Ukrainian artist Alexei Shovkunenko.