Since 1973, Dom Museum Wien has been located in the former residence of the Cathedral Provost, in the Zwettlerhof building. This historic building is situated between Stephansplatz and Wollzeile, right in the heart of Vienna: Where the intellectual and spiritual center of the city meets the secular hustle and bustle of one of Vienna's busiest streets. The affiliative nature of the museum's location is literally and figuratively manifested by the two public passageways. 

The buidling's name dates back to the 14th century and is a testament to the efforts at the time to upgrade Vienna and St. Stephen's Church by creating an architectural and organisational center. The name derives from the Zwettl Monastery, which came to own the building (which was first erected in 1244) in 1303, after the original Zwettl building had to make way for the new construction of St. Stephen's apse. In 1361, Duke Rudolf IV. took over Zwettlerhof in a trade-off, as he required residences for the provost and canons of the new collegiate church he had just establiched at St. Stephen's. In order to accommodate them, he funded the renovation (the first of many to take place over the course of the centuries) of the building. It remained the property of the collegiate church, and finally of the archbishopric. In the 19th century, the historic structure was torn down and rebuilt in 1844, which is when the passageways were constructed that remain iconic landmarks of the city center to this day. 

When Dom Museum Wien was relocated to the first floor of Zwettlerhof in 1973, it moved to a location imbued with a strong visual and spatial connection to the Cathedral and the city.