IIRC, Abraham Ibn Ezrah mentions in his interpretation of the Book of Ester that:
"והנה אין במגילה הזאת זכר ה', והיא מספרי הקודש?" (How come that God's name is not mentioned in the Book and it is still [considered] holy?)
I'm aware that the Gemmarah interprets various hints to God in different verses, but I don't recall it explicitly mentioning that God's names or Kinuyim are not written.
The Book of Ester WIKI page mentions that in the Septuagint version there were mentions of God's name, while the Masoretic versions lacks it.
So, what is the earliest source that explicitly states the disappearance of the names of God in the Book of Ester?
See also Wiki source here, and WIKIpedia here.