A good question. The Aramaic Targum repeats the ambiguity of the passage, "אנא ועולימתי נצום" (Me and my young women will fast), and there is almost no discussion of this issue in the classic biblical commentaries.
The only explanation I could find was in Ibn Ezra (in his second commentary to Esther), who writes that these girls are "השפחות" (the female slaves/handmaidens to Queen Esther). Thus, they were likely "the seven suitable girls who were given to her from the king's house" (Es. 2:9, and as noted by Cnsersmoit).
According to the commentaries and midrashim on 2:9, these were Persian girls who were not Jewish, but chosen for their virtue and good character. There is a midrash that Esther arranged every girl to see her one day a week, so that the Shabbat girl would not think anything strange and assume Esther rested all week long.
The Me'am Lo'ez for Esther (written by Rabbi Raphael Chiyya Pontremoli in the 1860s), in reference to the Yaarot Devash, describes the palace women's understanding of Esther in a way that would aptly fit her handmaiden's understanding of the command to fast:
[The women] did not know enough about Judaism to realize that this was the reason for her actions. They knew that she was an aristocratic stranger with a good chance of being queen, and they assumed that her idiosyncrasies were part of the image that she was trying to protect.