It is somewhat surprising that for a melody as ubiquitous as this, it was composed as recently as 1936. The Russian-born composer Ephraim Abileah originally wrote it as part of his modern Zionist oratorio "Chag Hacherut", the festival of freedom. As far as we know, the full oratorio was only ever performed once, in Haifa, but the melody for Ma Nishtana went on to become one of the most well known Jewish melodies after it was published in songsters, and broadcast on Israeli Radio.
This arrangement follows Abileah's original score. There are several small variations to how Ma Nishtana is often sung nowadays: the scale is pentatonic – and doesn't trace the now expected dominant chord on "mikol haleilot", Abileah's word stresses are slightly different, some pitches have altered over time, and overall it is structurally slightly different: Abileah calls for "halailah hazeh" four times followed by "kulo matza" twice (or equivalent for the subsequent verses), and each verse begins with "ma nishtana" in Abileah's score, rather than skipping to "sheb'chol".