The first Kleist Museum in Frankfurt (Oder) was set up at the suggestion of the Kleist Society in 1922-1923 on the ground floor of Heinrich von Kleist's birthplace, which is no longer preserved. The Kleist Museum is dedicated to the life and work of the poet Heinrich von Kleist (1777–1811), who was born in Frankfurt (Oder).

The building of today's Kleist Museum, planned in 1777 on the initiative of Prince Leopold of Braunschweig-Wolfenbüttel (1752 - 1785) as a garrison school and erected by the Frankfurt building inspector Friedrich Martin Knoblauch (1714 - 1791) at a cost of 3000 thalers, was opened on January 26 opened in 1778. Stylistically, the house with the low base and the wall templates (colossal pilasters) extending over two floors can be assigned to the last period of the late Baroque, the so-called Zopfstil. In the former free school, the children of the soldiers stationed in the city were taught according to the example of the country school set up by the philanthropist Eberhard von Rochow in Reckahn. In the 1920s the school closed.

The Kleist Museum was established in 1969 in the building of the former garrison school. In the now opened, modern, light-flooded and spacious museum extension, which was placed next to the beautiful baroque individual monument, the more than 34,000 units in the library and the collections - currently the most extensive documentation on Heinrich von Kleist and his literary-historical environment - are now finally being preserved Adequate storage and significantly improved presentation options available. The museum continues to be committed to the legacy of the poets Ewald Christian and Franz Alexander von Kleist as well as Caroline and Friedrich de la Motte Fouqué. The Kleist Museum is listed in the Federal Government's Blue Book as a cultural memorial site of national importance.

Since January 1, 2019, the house has been run as the Kleist Museum Foundation.

In the garden of the museum there are sculptures that bear witness to the engagement of important sculptors such as Wieland Förster or Werner Stötzer with the work of Heinrich von Kleist. In addition to a copy of Heinrich von Kleist's gravestone - the original is in the Stiftung Stadtmuseum Berlin - a replica of the grave cross (around 1977) of Ulrike von Kleist (1774 - 1849) and the gravestone of Christian Ernst Martini (1762 - 1833) were found in the garden lineup.