Short answer
Yes. Taraweeh is a separate sunnah of Ramadan nights and does not depend on the fast. A traveller who has stopped, a sick person who could not fast, or even someone who wrongly missed the fast should still pray it. Only a woman on her period or with postnatal bleeding does not pray.
Taraweeh is sunnah mu'akkadah for men and women in Ramadan, whether or not they fasted that day. Missing the fast, even without an excuse, does not cancel the sunnah of taraweeh; each is a separate act of worship.
The four schools agree on this.
Explanation
The fast is worship of the day and taraweeh is worship of the night. The Prophet ﷺ said that whoever stands in prayer in Ramadan out of faith and hoping for reward will have his past sins forgiven. He did not tie this to having fasted that day.
Who should still pray taraweeh:
- A traveller who is not fasting, once he has stopped and can pray in peace.
- A sick person who cannot fast but can pray, sitting if needed.
- An elderly person who pays fidya instead of fasting.
- Someone who skipped the fast without a reason. That is a sin that needs repentance and a make-up day, but leaving taraweeh as well does not help. Pray, repent and fast tomorrow.
Who does not pray it. A woman on her period or in postnatal bleeding does not pray at all, so she does not pray taraweeh and does not make it up. She can still make dhikr and dua and listen to the Quran. See periods in Ramadan.
Children are encouraged to join taraweeh to get used to it, without pressure. The four schools agree that taraweeh does not depend on the day's fast. For how to pray it, see how to pray taraweeh and taraweeh at home.
The evidence
Quran, Surah Al-Muzzammil 73:20
۞ إِنَّ رَبَّكَ يَعْلَمُ أَنَّكَ تَقُومُ أَدْنَىٰ مِن ثُلُثَىِ ٱلَّيْلِ وَنِصْفَهُۥ وَثُلُثَهُۥ وَطَآئِفَةٌۭ مِّنَ ٱلَّذِينَ مَعَكَ ۚ وَٱللَّهُ يُقَدِّرُ ٱلَّيْلَ وَٱلنَّهَارَ ۚ عَلِمَ أَن لَّن تُحْصُوهُ فَتَابَ عَلَيْكُمْ ۖ فَٱقْرَءُوا۟ مَا تَيَسَّرَ مِنَ ٱلْقُرْءَانِ ۚ عَلِمَ أَن سَيَكُونُ مِنكُم مَّرْضَىٰ ۙ وَءَاخَرُونَ يَضْرِبُونَ فِى ٱلْأَرْضِ يَبْتَغُونَ مِن فَضْلِ ٱللَّهِ ۙ وَءَاخَرُونَ يُقَٰتِلُونَ فِى سَبِيلِ ٱللَّهِ ۖ فَٱقْرَءُوا۟ مَا تَيَسَّرَ مِنْهُ ۚ وَأَقِيمُوا۟ ٱلصَّلَوٰةَ وَءَاتُوا۟ ٱلزَّكَوٰةَ وَأَقْرِضُوا۟ ٱللَّهَ قَرْضًا حَسَنًۭا ۚ وَمَا تُقَدِّمُوا۟ لِأَنفُسِكُم مِّنْ خَيْرٍۢ تَجِدُوهُ عِندَ ٱللَّهِ هُوَ خَيْرًۭا وَأَعْظَمَ أَجْرًۭا ۚ وَٱسْتَغْفِرُوا۟ ٱللَّهَ ۖ إِنَّ ٱللَّهَ غَفُورٌۭ رَّحِيمٌۢ ﴿٢٠﴾
Indeed, your Lord knows, [O Muhammad], that you stand [in prayer] almost two thirds of the night or half of it or a third of it, and [so do] a group of those with you. And Allah determines [the extent of] the night and the day. He has known that you [Muslims] will not be able to do it and has turned to you in forgiveness, so recite what is easy [for you] of the Qur'an. He has known that there will be among you those who are ill and others traveling throughout the land seeking [something] of the bounty of Allah and others fighting for the cause of Allah. So recite what is easy from it and establish prayer and give zakah and loan Allah a goodly loan. And whatever good you put forward for yourselves - you will find it with Allah. It is better and greater in reward. And seek forgiveness of Allah. Indeed, Allah is Forgiving and Merciful.
Night prayer is its own act of worship.
Sahih al-Bukhari 37
Sahih... من قام رمضان إيمانا واحتسابا غفر له ما تقدم من ذنبه ...
"Whoever stands in prayer in Ramadan out of faith and hoping for reward will have his past sins forgiven."
The reward of Ramadan's night prayer is promised without a condition of fasting.
Where the ruling is recorded
- Radd al-Muhtar (Ibn Abidin), Kitab al-Salah, chapter on witr and voluntary prayers, section on taraweeh. Taraweeh is an emphasised sunnah for men and women.
- Nur al-Idah with Maraqi al-Falah, Kitab al-Salah, chapter on taraweeh. Taraweeh is an emphasised sunnah prayed in Ramadan after Isha.
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.