EMST first operated, from 2000 to September 2003, on the ground floor of approximately 1,800 square meters, of the old Fix brewery, an example of post-war industrial architecture designed by Takis Zenetos. It is located in close proximity to the center of Athens as well as the archaeological sites of the city, including the Acropolis and the Acropolis Museum. As of 2020, the restoration of the building is in progress in order to create state of the art facilities for the permanent collection, periodic exhibitions, educational programs, and workshops. After an international architectural competition was announced, the architectural office which won the first prize and will realize the renovation of the Fix building are 3SK Stylianidis Architects in collaboration with Ioannis Mouzakis and associates architects LTD – studies of technical works Pan. Babilis and associates, and INSTA.

Until the return of the museum to the Fix building, EMST will continue its exhibitions program in the spaces of the Athens Conservatory, one of the most prestigious cultural institutions and finest buildings of architecture in the capital. By 2020, the Greek government spent 40 million euros on the museum, with the Stavros Niarchos Foundation giving a further 3 million euros in the final push towards completion. In the meantime, the delays in the museum’s opening cost EMST a 3.3 million dollars subsidy from the European Union. Ownership of the Fix building was transferred from the subway authority Attica Metro, which owned the former brewery since the 1990s, to the museum foundation.