Sheikh Sulaymân al-Tuwayjirî
It is obligatory on the woman who possesses money to pay her own Zakâh. She must know that in Islamic Law, she is the one responsible for managing her own personal finances. If the money in her possession is enough to make her liable to pay Zakâh, then she must pay it.
For money, she is liable to pay 2.5%. If she possesses $10,000, for instance, she is liable to pay $250.
Her husband’s finances have nothing to do with her’s, so his debt has no affect on her Zakâh.
Source: Islam Today