Short answer
Muslims believe Allah revealed a scripture called the Injil (Gospel) to Isa (Jesus), with guidance and light in it. But the Injil is not the same as the New Testament, which is a collection of later writings about Jesus by others. Muslims accept what agrees with the Quran, reject what contradicts it, and suspend judgement on the rest.
Belief that Allah revealed the Injil to Isa is part of belief in the revealed books. Sunni scholars hold that it was not preserved as it was sent, so the Quran is the criterion over earlier scripture, and the Bible is not a source of Islamic belief or law.
The four schools agree on this.
Explanation
The Quran says Allah sent Isa "confirming that which came before him in the Torah; and We gave him the Gospel, in which was guidance and light" (5:46). For Muslims the Injil is a book revealed by Allah to Isa himself, in the same way the Torah was revealed to Musa and the Quran to Muhammad ﷺ.
The New Testament is something different. Its four Gospels are accounts of Jesus's life written by later authors, and most of the rest is letters by Paul and others. Christians themselves do not claim it is a book dictated to Jesus. So when Muslims say they believe in the Injil, they do not mean every word of the New Testament as it is printed today.
The Quran describes itself as "confirming that which preceded it of the Scripture and as a criterion over it" (5:48). It agrees with the Gospels on much: the virgin birth, Isa's miracles, his title of Messiah and his call to worship one God. It rejects the claim that he is divine and that he was crucified (4:157). Where the Bible says something the Quran neither confirms nor denies, the Prophet ﷺ told us not to believe it and not to call it a lie.
For more, read do Muslims believe in the Torah?, can Muslims read the Bible? and Islam and Christianity.
The evidence
Quran, Surah Al-Maaida 5:46
وَقَفَّيْنَا عَلَىٰٓ ءَاثَٰرِهِم بِعِيسَى ٱبْنِ مَرْيَمَ مُصَدِّقًۭا لِّمَا بَيْنَ يَدَيْهِ مِنَ ٱلتَّوْرَىٰةِ ۖ وَءَاتَيْنَٰهُ ٱلْإِنجِيلَ فِيهِ هُدًۭى وَنُورٌۭ وَمُصَدِّقًۭا لِّمَا بَيْنَ يَدَيْهِ مِنَ ٱلتَّوْرَىٰةِ وَهُدًۭى وَمَوْعِظَةًۭ لِّلْمُتَّقِينَ ﴿٤٦﴾
And We sent, following in their footsteps, Jesus, the son of Mary, confirming that which came before him in the Torah; and We gave him the Gospel, in which was guidance and light and confirming that which preceded it of the Torah as guidance and instruction for the righteous.
Affirms that Allah revealed the Injil to Isa.
Quran, Surah Al-Maaida 5:48
وَأَنزَلْنَآ إِلَيْكَ ٱلْكِتَٰبَ بِٱلْحَقِّ مُصَدِّقًۭا لِّمَا بَيْنَ يَدَيْهِ مِنَ ٱلْكِتَٰبِ وَمُهَيْمِنًا عَلَيْهِ ۖ فَٱحْكُم بَيْنَهُم بِمَآ أَنزَلَ ٱللَّهُ ۖ وَلَا تَتَّبِعْ أَهْوَآءَهُمْ عَمَّا جَآءَكَ مِنَ ٱلْحَقِّ ۚ لِكُلٍّۢ جَعَلْنَا مِنكُمْ شِرْعَةًۭ وَمِنْهَاجًۭا ۚ وَلَوْ شَآءَ ٱللَّهُ لَجَعَلَكُمْ أُمَّةًۭ وَٰحِدَةًۭ وَلَٰكِن لِّيَبْلُوَكُمْ فِى مَآ ءَاتَىٰكُمْ ۖ فَٱسْتَبِقُوا۟ ٱلْخَيْرَٰتِ ۚ إِلَى ٱللَّهِ مَرْجِعُكُمْ جَمِيعًۭا فَيُنَبِّئُكُم بِمَا كُنتُمْ فِيهِ تَخْتَلِفُونَ ﴿٤٨﴾
And We have revealed to you, [O Muhammad], the Book in truth, confirming that which preceded it of the Scripture and as a criterion over it. So judge between them by what Allah has revealed and do not follow their inclinations away from what has come to you of the truth. To each of you We prescribed a law and a method. Had Allah willed, He would have made you one nation [united in religion], but [He intended] to test you in what He has given you; so race to [all that is] good. To Allah is your return all together, and He will [then] inform you concerning that over which you used to differ.
Makes the Quran the judge over earlier scripture.
Sahih al-Bukhari 4485
Sahih... لاَ تُصَدِّقُوا أَهْلَ الْكِتَابِ وَلاَ تُكَذِّبُوهُمْ، وَقُولُوا آمَنَّا بِاللَّهِ وَمَا أُنْزِلَ ...
"Do not believe the People of the Book and do not call them liars. Say: We believe in Allah and in what has been sent down."
Gives the rule for Biblical reports the Quran neither confirms nor denies.
Where the ruling is recorded
- al-Aqida al-Tahawiyya, Section on belief in the angels, prophets and books. States that Muslims believe in the books revealed to the messengers.
- al-Aqa'id al-Nasafiyya with Sharh al-Taftazani, Section on the revealed books. Affirms that Allah revealed books to His prophets, with His commands, prohibitions, promises and warnings.
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.