Praise be to Allah.
If a woman vows to fast for a month, then she should make up the days when she was menstruating, just as she makes up the days when she menstruates during the month of Ramadaan.
See al-Mughni by Ibn Qudaamah, 10/86.
The Standing Committee for Issuing Fatwas was asked this question and replied:
You have to fast the month which you vowed to fast, and if you break the fast during part of it because of menstruation, then you have to make up the number of days of that month when you did not fast.
And Allaah is the Source of strength. May Allaah send blessings and peace upon our Prophet Muhammad and his family and companions.
Fataawa al-Lajnah al-Daa’imah, 23/336.