Upvote:2
Gregory of Nyssa (335-395) wrote a complete commentary on the Song of Songs, though I can't tell whether his is the oldest complete Christian commentary. It has been translated by the Hellenic College Press in Boston. Ireneaus (b.130) comments briefly on a single verse in his 1st letter to the Ephesians (17).
I did not research Jewish commentaries but there are certainly many, many of these. The medieval commentary of Rashi at Chabad.org might be a place to start. Rashi (Shlomo Yitzchaki) himself lived from 1040 to 1105, but he references other older commentaries.