Source: Fatawa Aman Puri by Sheikh Ghulam Mustafa Zaheer Aman Puri
Question:
A Muslim has married a non-Muslim woman, will the dower (Mahr) be obligatory?
Answer:
Marriage with a non-Muslim woman other than the People of the Book is not permissible. This marriage is invalid; however, if one has secluded with a non-Muslim woman, she will be entitled to the full dowry, because in an invalid marriage where seclusion occurs, the dowry becomes obligatory.
❀ Sayyida Aisha (may Allah be pleased with her) narrates that the Messenger of Allah (peace be upon him) said:
أيما امرأة نكحت بغير إذن وليها فنكاحها باطل، فنكاحها باطل، فنكاحها باطل، فإن دخل بها فلها المهر بما استحل من فرجها
"Any woman who marries without the permission of her guardian, her marriage is invalid, her marriage is invalid, her marriage is invalid. If a man has intercourse with her, she will receive the dowry from him in exchange for making her private parts lawful to him."
Reference: (Musnad Ishaq: 499, Musnad Imam Ahmad: 165/6, Musnad Al-Humaydi: 228, Musnad Al-Tayalisi (Manha: 305/1), Sunan Abu Dawood: 2083, Sunan Ibn Majah: 1879, Sunan Al-Tirmidhi: 1102, Al-Sunan Al-Kubra for Al-Nasa'i: 5394, Musnad Abu Ya'la: 2083, Sunan Al-Daraqutni: 221/3, Al-Sunan Al-Kubra for Al-Bayhaqi: 105/7, and its chain is good)
Thus, a non-Muslim woman is entitled to the full dowry and she can also demand it.