With fasting a means to be closer to God in some way, to stand in His Presence for serious petition or just presence, I would personally say no.
Women are Biblically, old testament levitical law style, ritually unclean during our menstrual cycle.
While there's no specific law concerning this in the New Covenant we often extrapolate from the principals we find in the old testament.
In one respect, we are all ritually unclean and unworthy to stand before God and ask anything from Him however, we are all, those who believe, made clean by the blood of Jesus and His sacrifice in order to stand in His Presence.
But on the other hand, God is unchanging and since fasting is a special and specific thing I would definitely wait until my menstrual cycle is over for that, as a matter of respect for God.
Since there's no written rules about it under the New Covenant though, it will fall under liberty of conscious.
You may want to consider biological reasons for not wanting to fast at the same time as your menstrual cycle though.