Short answer
No. A Muslim man may marry only a Muslim woman or a believing Christian or Jewish woman, and a Muslim woman may marry only a Muslim man. An atheist, agnostic or person with no religion is neither, so the nikah would not be valid, even if they come from a Christian family. The four schools agree.
Nikah between a Muslim and someone who is neither Muslim nor of the People of the Book is void. A person who rejects God or all revealed religion is not counted among the People of the Book, whatever their family background, and a Muslim woman may not marry any non-Muslim man.
The four schools agree on this.
Explanation
Allah says, "do not marry polytheistic women until they believe" (2:221), and "hold not to marriage bonds with disbelieving women" (60:10). The one exception is for a man marrying chaste women "from among those who were given the Scripture" (5:5), that is, Christian and Jewish women. Everyone else is outside that permission.
Who counts as People of the Book? Someone who believes in God and follows a revealed scripture, Christian or Jewish, even if not very practising. A person raised Christian who now says they do not believe in God, or who rejects all religion, no longer counts. See who are the People of the Book.
- Atheist or agnostic: no.
- "Spiritual but not religious": usually no, unless they truly hold to Christianity or Judaism. Ask a mufti.
- Hindu, Sikh, Buddhist, pagan and others: no. See marrying a Hindu.
- A Muslim woman: may marry only a Muslim man. See why.
If you love someone who has no faith, share Islam with them honestly and give them time, but do not push for a conversion they do not believe in. See converting to marry. If you are already in such a marriage, or became Muslim while married, see a convert whose spouse is not Muslim and ask a mufti.
The evidence
Quran, Surah Al-Baqara 2:221
وَلَا تَنكِحُوا۟ ٱلْمُشْرِكَٰتِ حَتَّىٰ يُؤْمِنَّ ۚ وَلَأَمَةٌۭ مُّؤْمِنَةٌ خَيْرٌۭ مِّن مُّشْرِكَةٍۢ وَلَوْ أَعْجَبَتْكُمْ ۗ وَلَا تُنكِحُوا۟ ٱلْمُشْرِكِينَ حَتَّىٰ يُؤْمِنُوا۟ ۚ وَلَعَبْدٌۭ مُّؤْمِنٌ خَيْرٌۭ مِّن مُّشْرِكٍۢ وَلَوْ أَعْجَبَكُمْ ۗ أُو۟لَٰٓئِكَ يَدْعُونَ إِلَى ٱلنَّارِ ۖ وَٱللَّهُ يَدْعُوٓا۟ إِلَى ٱلْجَنَّةِ وَٱلْمَغْفِرَةِ بِإِذْنِهِۦ ۖ وَيُبَيِّنُ ءَايَٰتِهِۦ لِلنَّاسِ لَعَلَّهُمْ يَتَذَكَّرُونَ ﴿٢٢١﴾
And do not marry polytheistic women until they believe. And a believing slave woman is better than a polytheist, even though she might please you. And do not marry polytheistic men [to your women] until they believe. And a believing slave is better than a polytheist, even though he might please you. Those invite [you] to the Fire, but Allah invites to Paradise and to forgiveness, by His permission. And He makes clear His verses to the people that perhaps they may remember.
Marriage to those outside Islam and the People of the Book is forbidden.
Quran, Surah Al-Mumtahana 60:10
يَٰٓأَيُّهَا ٱلَّذِينَ ءَامَنُوٓا۟ إِذَا جَآءَكُمُ ٱلْمُؤْمِنَٰتُ مُهَٰجِرَٰتٍۢ فَٱمْتَحِنُوهُنَّ ۖ ٱللَّهُ أَعْلَمُ بِإِيمَٰنِهِنَّ ۖ فَإِنْ عَلِمْتُمُوهُنَّ مُؤْمِنَٰتٍۢ فَلَا تَرْجِعُوهُنَّ إِلَى ٱلْكُفَّارِ ۖ لَا هُنَّ حِلٌّۭ لَّهُمْ وَلَا هُمْ يَحِلُّونَ لَهُنَّ ۖ وَءَاتُوهُم مَّآ أَنفَقُوا۟ ۚ وَلَا جُنَاحَ عَلَيْكُمْ أَن تَنكِحُوهُنَّ إِذَآ ءَاتَيْتُمُوهُنَّ أُجُورَهُنَّ ۚ وَلَا تُمْسِكُوا۟ بِعِصَمِ ٱلْكَوَافِرِ وَسْـَٔلُوا۟ مَآ أَنفَقْتُمْ وَلْيَسْـَٔلُوا۟ مَآ أَنفَقُوا۟ ۚ ذَٰلِكُمْ حُكْمُ ٱللَّهِ ۖ يَحْكُمُ بَيْنَكُمْ ۚ وَٱللَّهُ عَلِيمٌ حَكِيمٌۭ ﴿١٠﴾
O you who have believed, when the believing women come to you as emigrants, examine them. Allah is most knowing as to their faith. And if you know them to be believers, then do not return them to the disbelievers; they are not lawful [wives] for them, nor are they lawful [husbands] for them. But give the disbelievers what they have spent. And there is no blame upon you if you marry them when you have given them their due compensation. And hold not to marriage bonds with disbelieving women, but ask for what you have spent and let them ask for what they have spent. That is the judgement of Allah; He judges between you. And Allah is Knowing and Wise.
A Muslim may not stay married to a disbelieving woman.
Quran, Surah Al-Maaida 5:5
ٱلْيَوْمَ أُحِلَّ لَكُمُ ٱلطَّيِّبَٰتُ ۖ وَطَعَامُ ٱلَّذِينَ أُوتُوا۟ ٱلْكِتَٰبَ حِلٌّۭ لَّكُمْ وَطَعَامُكُمْ حِلٌّۭ لَّهُمْ ۖ وَٱلْمُحْصَنَٰتُ مِنَ ٱلْمُؤْمِنَٰتِ وَٱلْمُحْصَنَٰتُ مِنَ ٱلَّذِينَ أُوتُوا۟ ٱلْكِتَٰبَ مِن قَبْلِكُمْ إِذَآ ءَاتَيْتُمُوهُنَّ أُجُورَهُنَّ مُحْصِنِينَ غَيْرَ مُسَٰفِحِينَ وَلَا مُتَّخِذِىٓ أَخْدَانٍۢ ۗ وَمَن يَكْفُرْ بِٱلْإِيمَٰنِ فَقَدْ حَبِطَ عَمَلُهُۥ وَهُوَ فِى ٱلْءَاخِرَةِ مِنَ ٱلْخَٰسِرِينَ ﴿٥﴾
This day [all] good foods have been made lawful, and the food of those who were given the Scripture is lawful for you and your food is lawful for them. And [lawful in marriage are] chaste women from among the believers and chaste women from among those who were given the Scripture before you, when you have given them their due compensation, desiring chastity, not unlawful sexual intercourse or taking [secret] lovers. And whoever denies the faith - his work has become worthless, and he, in the Hereafter, will be among the losers.
The only exception is for Christian and Jewish women.
Sahih al-Bukhari 5090
Sahih... تنكح المرأة لأربع لمالها ولحسبها ولجمالها ولدينها فاظفر بذات الدين ...
"A woman is married for four things: her wealth, her family, her beauty and her religion. Win the one with religion."
Faith is the first thing to look for in a spouse.
Where the ruling is recorded
- al-Hidaya, Kitab al-Nikah, Fasl fi Bayan al-Muharramat. Marriage to a woman who is neither Muslim nor of the People of the Book is not permitted.
- Radd al-Muhtar (Ibn Abidin), Kitab al-Nikah, Fasl fi al-Muharramat. Who counts as a person of the Book: one who believes in a prophet and a revealed scripture.
Checked by our team. For a more accurate answer to your own situation, consult a scholar. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.