It is permissible for one who is sick not to fast in Ramadaan, because Allaah says (interpretation of the meaning):
“but if any of you is ill or on a journey, the same number (should be made up) from other days”
This has to do with severe illness where it is too difficult to fast.
With regard to mild illness where it is not too difficult to fast, this is not regarded as an excuse not to fast in Ramadaan.
See also question no. 12488
If the migraine makes it too difficult for her to fast, then it is permissible for her not to fast, and she should make up the days that she missed after Ramadaan.
If this migraine is continuous and she cannot make up the fasts, then she should feed one poor person for each day that she did not fast.
And Allaah knows best.