Question:

If a woman’s period starts whilst fasting, is she allowed to eat thereafter?

Answer:

In the Name of Allah, the Most Gracious, the Most Merciful.

As-salāmu ‘alaykum wa-rahmatullāhi wa-barakātuh.

If a woman was fasting and her menses began, then it is permissible for her to eat and drink during the rest of the day.  Likewise, it is permissible for her to eat during the days of her menses when she is not fasting.  She should eat discreetly; away from the sight of others.[1] 

If a woman becomes pure from her menses during the day in Ramadhan, then she must abstain from eating and drinking like others.[2]
 
And Allah Ta’āla Knows Best
Mufti Faraz Adam,
www.darulfiqh.com