Because of the saying of Allah, the Mighty and Majestic: "They (the believing women) are not lawful for them (the disbelievers), nor are they (the disbelievers) lawful for them." [Surah al-Mumtahanah: 10]
And because of the saying of Allah Almighty: "And do not hold on to the marriage ties of disbelieving women." [Surah al-Mumtahanah: 10]
Hadith Referenceالسنن الكبرى للبيهقي / كتاب النكاح / Q14061
Ibn Ishaq mentions the story of Abu al-As bin al-Rabi', who set out while still in a state of polytheism, and that his wife Zaynab (may Allah be pleased with her), the daughter of the Messenger of Allah (peace and blessings be upon him), was in Madinah. He said: Yazid bin Ruman narrated from Urwah, from Sayyidah Aishah (may Allah be pleased with her), that Sayyidah Zaynab (may Allah be pleased with her) called out: "O people, I have given protection to Abu al-As bin al-Rabi'." The narrator mentioned the hadith; then the Messenger of Allah (peace and blessings be upon him) came to his daughter Zaynab (may Allah be pleased with her) and said: "O my daughter, give him an honourable lodging, but let him not come in to you, for you are not lawful for him." [Da'if (weak)]
Hadith Referenceالسنن الكبرى للبيهقي / كتاب النكاح / 14061