A fugue is a musical piece that begins with some theme and then comes back to that theme several times, with variations. We don't know of any other "fugue" poems, certainly not any famous ones. It would be as if someone took a Viennese Waltz and said, "I'm going to find a way to make this into a literary form."
The poem basically restates its "theme" four times. Each time begins with the invocation to "black milk," and then a description of the man who lives in a house. The end of each stanza is choppier and mixes together different phrases, like "your golden hair Marguerite, your ashen hair Shulamith." Celan does not use much punctuation and he does not write in complete sentences. Instead, he splices together snippets of language that only have a slight connection to one another. This gives the poem an almost schizophrenic feel: indeed, a "fugue" in psychology is a disoriented state that resembles schizophrenia (source). The poem doesn't have any regular rhythm scheme, and it is translated from German so the rhythm of the English translation is only an approximation.
The fugue is an interesting form to choose because it is so closely associated with German high culture. Germany (and its German-speaking neighbor, Austria) certainly has one of the most impressive musical cultures in the world. Just think of all those "big names" of music: Wagner, Beethoven, Mozart, Strauss, etc. But Celan takes this classy, cultured tradition and uses it in a poem about death and concentration camps. It's as if he wanted to implicate the German musical tradition in the Holocaust. By far the most famous composer to use the fugue is J.S. Bach, who lived in the seventeenth century and wrote The Art of the Fugue, a collection of incredibly complicated and beautiful fugues.