Short answer
Yes. Nuh (Noah) is one of the great messengers of Allah, and the Quran tells his story in detail. He called his people to Allah for 950 years, built the ark by Allah's command, and was saved with the believers while the disbelievers drowned in the flood. One of his own sons refused to board and drowned.
Belief in Nuh as a prophet and messenger is part of iman, and the story of the ark and the flood is true as the Quran tells it. Whether the flood covered the whole earth or only the land of his people is something the scholars discussed; the Quran's account itself must be accepted.
The four schools agree on this.
Explanation
"We certainly sent Noah to his people, and he remained among them a thousand years minus fifty years, and the flood seized them while they were wrongdoers" (29:14). Surah Nuh records his patient call, day and night, in public and in private, and how his people put their fingers in their ears. When Allah told him that no more of them would believe, He commanded him to build the ark.
When the command came, Nuh was told to "load upon the ship of each [creature] two mates and your family" and the believers (11:40). The ark sailed through waves like mountains. Nuh called to his son to come aboard, but he said he would climb a mountain, and he drowned (11:42-43). Nuh's wife was also among the disbelievers (66:10). Then the water subsided "and the ship came to rest on the [mountain of] Judiyy" (11:44). The lesson: family ties do not save anyone; faith does.
The Prophet ﷺ said that on the Day of Judgement Nuh will be asked whether he conveyed the message, and the ummah of Muhammad ﷺ will testify for him. In the hadith of intercession, people will come to Nuh and say: you are the first of the messengers to the people of the earth.
Was the flood worldwide? Many classical commentators held that it covered the earth, since Nuh's people were then the whole of mankind; some later scholars held it covered the land of his people. Muslims affirm what the Quran says and leave the rest to Allah. Read the full story of Prophet Nuh and Surah Nuh.
The evidence
Quran, Surah Al-Ankaboot 29:14
وَلَقَدْ أَرْسَلْنَا نُوحًا إِلَىٰ قَوْمِهِۦ فَلَبِثَ فِيهِمْ أَلْفَ سَنَةٍ إِلَّا خَمْسِينَ عَامًۭا فَأَخَذَهُمُ ٱلطُّوفَانُ وَهُمْ ظَٰلِمُونَ ﴿١٤﴾
And We certainly sent Noah to his people, and he remained among them a thousand years minus fifty years, and the flood seized them while they were wrongdoers.
Gives the length of Nuh's call.
Quran, Surah Hud 11:40
حَتَّىٰٓ إِذَا جَآءَ أَمْرُنَا وَفَارَ ٱلتَّنُّورُ قُلْنَا ٱحْمِلْ فِيهَا مِن كُلٍّۢ زَوْجَيْنِ ٱثْنَيْنِ وَأَهْلَكَ إِلَّا مَن سَبَقَ عَلَيْهِ ٱلْقَوْلُ وَمَنْ ءَامَنَ ۚ وَمَآ ءَامَنَ مَعَهُۥٓ إِلَّا قَلِيلٌۭ ﴿٤٠﴾
[So it was], until when Our command came and the oven overflowed, We said, "Load upon the ship of each [creature] two mates and your family, except those about whom the word has preceded, and [include] whoever has believed." But none had believed with him, except a few.
Describes the boarding of the ark.
Quran, Surah Hud 11:44
وَقِيلَ يَٰٓأَرْضُ ٱبْلَعِى مَآءَكِ وَيَٰسَمَآءُ أَقْلِعِى وَغِيضَ ٱلْمَآءُ وَقُضِىَ ٱلْأَمْرُ وَٱسْتَوَتْ عَلَى ٱلْجُودِىِّ ۖ وَقِيلَ بُعْدًۭا لِّلْقَوْمِ ٱلظَّٰلِمِينَ ﴿٤٤﴾
And it was said, "O earth, swallow your water, and O sky, withhold [your rain]." And the water subsided, and the matter was accomplished, and the ship came to rest on the [mountain of] Judiyy. And it was said, "Away with the wrongdoing people."
Tells where the ark came to rest.
Sahih al-Bukhari 3339
Sahih... يَجِيءُ نُوحٌ وَأُمَّتُهُ فَيَقُولُ اللَّهُ تَعَالَى هَلْ بَلَّغْتَ ...
"Nuh and his people will come, and Allah will ask: Did you convey the message?"
Shows Nuh's standing on the Day of Judgement.
Sahih al-Bukhari 3340
Sahih... يَا نُوحُ أَنْتَ أَوَّلُ الرُّسُلِ إِلَى أَهْلِ الأَرْضِ ...
"O Nuh, you are the first of the messengers to the people of the earth."
Shows Nuh's rank among the messengers.
Where the ruling is recorded
- Tafsir Ibn Kathir, Commentary on Surah Hud, the story of Nuh. Explains the building of the ark, the flood and the fate of his son.
- Ma'arif al-Quran (Mufti Muhammad Shafi), Commentary on Surah Hud and Surah Nuh. Explains the story and its lessons.
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.