In your works-cited-list entry, provide the name of a foreign institution in the original language if that is how it is presented in your source. In the following example, the publisher’s name is given in the original language:

Dieulafoy, Jane. Papiers et correspondance de Marcel et Jane Dieulafoy. Manuscripts de la Bibliothèque de l’Institut de France, Paris. 

Names of  institutions in languages that do not use the Roman alphabet (Russian, Greek, Hebrew, etc.) are almost always presented in transliteration. In this example, the publisher’s name is given in transliteration:

Šklovskij, Viktor. Жизнь художника Федотова [The Life of the Artist Fedotov]. Izdatelʹstvo detskoy literatury, 1936.

In your prose, you do not need to provide a translation for the name of an institution given in the original language: 

She gave a speech before the Fondo de Cultura Económica.

They spent twelve hours a day at the Bibliothèque Nationale.

He works for the Russian publisher Izdatelʹstvo detskoy literatury.

In the above example, note that in MLA style, names of non-English institutions are capitalized like titles of works in English, but names of Russian institutions are capitalized like a sentence.