The MMK was founded in 1981. After an eight-year planning and construction phase, it opened in June 1991 under Jean-Christophe Ammann as director.

The bomb attacks on Frankfurt during World War II destroyed large sections of the historical urban centre. In the 1970s, the city carried out extensive planning and construction measures in an effort to reorganize Frankfurt's cultural landscape – deliberations that also played a major role in the creation of the Museumsufer (Museum Embankment). The founding of a museum of modern art also dates back to the era of Hilmar Hoffmann, the head of the city’s department of culture at the time. From 1981, the art historian and theatre critic Peter Iden was the museum’s interim director.

The choice of location for the museum was made in 1982 in favour of a vacant lot that had previously been intended for municipal offices. After an open competition for the planning of the museum building, the Viennese architect Hans Hollein was commissioned with the project on 17 May 1983. Hollein's design took several premises into consideration: the integration of the new building into the urban environment by way of the exterior material and colour design, the spatial challenge of the triangular site, which defined the floor space, and the museological concept, which on the one hand had to accommodate functional necessities while on the other hand doing justice to the art that would fill the interior. The building was to provide ideal conditions for art presentation and hold an appeal for the public.

The city of Frankfurt had acquired a large proportion of the collection of Karl Ströher, an industrialist of Darmstadt, in 1981. With their focus on American Pop and Minimal Art, these holdings were to form the core of the MUSEUMMMK für Moderne Kunst. Hans Hollein was well acquainted with the collection and took this knowledge into account in his deliberations: He envisioned a museum without any neutral space, "but only characteristic spaces of different dimensions (and their means of access), with which the artwork enters into a dialectic – in mutual potentiation". With this idea in mind, he succeeded in organizing the interior of the triangular building in such a way that a walk through it makes a lasting impression.

The building is arranged axially around a central hall illuminated from above. From here visitors can access all the various sections and floors of the museum, which comprises thirty exhibition galleries. The lighting and the suspenseful relationship between the individual, differently proportioned rooms compose the building’s rhythm. To this day, the museum is unique in its specific post-modern architecture. Here the visitor perceives architecture through art and art through architecture.