Short answer
Not in themselves, for women. But acrylics, gels, press-ons and nail glue cover the nail and stop water reaching it, so wudu and ghusl are not valid while they are on. A woman who prays would have to remove them before every wudu, so in practice they only suit times she is not praying, like her period. Men should not wear them.
Artificial nails are permitted adornment for a woman in principle, but they block water, so wudu and ghusl over them are invalid. A woman who is praying should not apply nails she cannot remove for each wudu.
The four schools agree on this.
Explanation
In wudu the hands must be washed fully, nails included. When a man left a dry patch the size of a nail on his foot, the Prophet ﷺ told him to go back and do his wudu properly. Any coating that sits on the nail and keeps water off it breaks this rule. The four schools agree that such a barrier must come off.
The types. Acrylics, gels, dip powder, press-ons with glue and nail wraps all cover the nail with a layer water cannot pass through. For wudu they are the same as nail polish; see can you pray with nail polish.
The ruling. Making yourself beautiful is good, and a woman may wear artificial nails at a time when she is not praying, such as during her period, provided she removes them, glue and all, before her ghusl. Acrylics and gels that need a salon to remove cannot come off before each wudu, so Hanafi muftis advise women who are praying not to get them. Press-ons that come off cleanly are easier, but they still have to come off for every wudu.
If you prayed with them. Wudu over them was not valid, so remove them, make wudu and make up those prayers. The qada calculator can help you count.
Other points. Very long or clawed nails also go against the Sunnah of keeping nails trimmed; see long nails. Henna on the nails leaves no layer and is a lovely alternative. Men should not wear artificial nails or nail polish.
The evidence
Quran, Surah Al-Maaida 5:6
يَٰٓأَيُّهَا ٱلَّذِينَ ءَامَنُوٓا۟ إِذَا قُمْتُمْ إِلَى ٱلصَّلَوٰةِ فَٱغْسِلُوا۟ وُجُوهَكُمْ وَأَيْدِيَكُمْ إِلَى ٱلْمَرَافِقِ وَٱمْسَحُوا۟ بِرُءُوسِكُمْ وَأَرْجُلَكُمْ إِلَى ٱلْكَعْبَيْنِ ۚ وَإِن كُنتُمْ جُنُبًۭا فَٱطَّهَّرُوا۟ ۚ وَإِن كُنتُم مَّرْضَىٰٓ أَوْ عَلَىٰ سَفَرٍ أَوْ جَآءَ أَحَدٌۭ مِّنكُم مِّنَ ٱلْغَآئِطِ أَوْ لَٰمَسْتُمُ ٱلنِّسَآءَ فَلَمْ تَجِدُوا۟ مَآءًۭ فَتَيَمَّمُوا۟ صَعِيدًۭا طَيِّبًۭا فَٱمْسَحُوا۟ بِوُجُوهِكُمْ وَأَيْدِيكُم مِّنْهُ ۚ مَا يُرِيدُ ٱللَّهُ لِيَجْعَلَ عَلَيْكُم مِّنْ حَرَجٍۢ وَلَٰكِن يُرِيدُ لِيُطَهِّرَكُمْ وَلِيُتِمَّ نِعْمَتَهُۥ عَلَيْكُمْ لَعَلَّكُمْ تَشْكُرُونَ ﴿٦﴾
O you who have believed, when you rise to [perform] prayer, wash your faces and your forearms to the elbows and wipe over your heads and wash your feet to the ankles. And if you are in a state of janabah, then purify yourselves. But if you are ill or on a journey or one of you comes from the place of relieving himself or you have contacted women and do not find water, then seek clean earth and wipe over your faces and hands with it. Allah does not intend to make difficulty for you, but He intends to purify you and complete His favor upon you that you may be grateful.
The hands must be washed fully in wudu, so a covering on the nails must be removed.
Sahih Muslim 243
Sahih... ارجع فأحسن وضوءك ...
"Go back and do your wudu properly."
Even a nail-sized dry spot makes wudu incomplete.
Where the ruling is recorded
- al-Durr al-Mukhtar with Radd al-Muhtar, Kitab al-Taharah, the obligations of wudu. A substance with a body, such as wax or dough, on the nails prevents wudu.
- al-Fatawa al-Hindiyya, Kitab al-Taharah, chapter on wudu. Water must reach every part that is washed.
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.