Short answer
No. Islam teaches that Adam and Hawwa (Eve) sinned, repented and were forgiven, and that no one carries the sin of another. Every child is born on the fitrah, a pure natural disposition, and becomes accountable only for his or her own choices after reaching maturity.
Sunni creed holds that sin is personal and is not inherited, based on the Quran's rule that no bearer of burdens bears another's burden. Adam's slip was forgiven, so there is no inherited guilt needing to be paid for by anyone's sacrifice.
The four schools agree on this.
Explanation
The Quran tells the story plainly. Adam and his wife ate from the tree, regretted it, and said: "Our Lord, we have wronged ourselves" (7:23). Then "Adam received from his Lord [some] words, and He accepted his repentance" (2:37), and "his Lord chose him and turned to him in forgiveness and guided [him]" (20:122). The matter was closed: there is no lasting stain passed on to his children.
The Quran states the principle more than once: "no bearer of burdens will bear the burden of another" (6:164, 53:38). Each person is judged for what he or she did. The Prophet ﷺ said every child is born on the fitrah; it is the parents who raise him as a Jew, a Christian or a Magian. A baby is not guilty of anything, and children who die young are in Jannah, as the scholars explain from the hadith.
Why did Adam come down to earth, then? Allah had already told the angels, before Adam was created, "I will make upon the earth a successive authority" (2:30). Earth was always the plan: a place of testing, with the way back to Jannah open through faith and good deeds. Salvation does not need a sacrifice for an inherited sin; it comes through belief, repentance and Allah's mercy.
How does this differ from Christian teaching? The doctrine of original sin holds that every human inherits a fallen nature from Adam, and that the death of Jesus on the cross atones for it. Islam teaches no inherited guilt, no need for an atonement in anyone's place, and a door of repentance open directly to Allah until death. That is also why Muslims do not believe Jesus died for anyone's sins; see what Islam says about Jesus.
Read more in did Adam and Eve sin, and what was the forbidden fruit?, how do Muslims get to Jannah? and do children who die go to Jannah?
The evidence
Quran, Surah Al-An'aam 6:164
قُلْ أَغَيْرَ ٱللَّهِ أَبْغِى رَبًّۭا وَهُوَ رَبُّ كُلِّ شَىْءٍۢ ۚ وَلَا تَكْسِبُ كُلُّ نَفْسٍ إِلَّا عَلَيْهَا ۚ وَلَا تَزِرُ وَازِرَةٌۭ وِزْرَ أُخْرَىٰ ۚ ثُمَّ إِلَىٰ رَبِّكُم مَّرْجِعُكُمْ فَيُنَبِّئُكُم بِمَا كُنتُمْ فِيهِ تَخْتَلِفُونَ ﴿١٦٤﴾
Say, "Is it other than Allah I should desire as a lord while He is the Lord of all things? And every soul earns not [blame] except against itself, and no bearer of burdens will bear the burden of another. Then to your Lord is your return, and He will inform you concerning that over which you used to differ."
States that sin is not inherited.
Quran, Surah Al-Baqara 2:37
فَتَلَقَّىٰٓ ءَادَمُ مِن رَّبِّهِۦ كَلِمَٰتٍۢ فَتَابَ عَلَيْهِ ۚ إِنَّهُۥ هُوَ ٱلتَّوَّابُ ٱلرَّحِيمُ ﴿٣٧﴾
Then Adam received from his Lord [some] words, and He accepted his repentance. Indeed, it is He who is the Accepting of repentance, the Merciful.
Shows Adam's sin was forgiven.
Sahih al-Bukhari 1385
Sahih... كُلُّ مَوْلُودٍ يُولَدُ عَلَى الْفِطْرَةِ، فَأَبَوَاهُ يُهَوِّدَانِهِ أَوْ يُنَصِّرَانِهِ ...
"Every child is born on the fitrah; then his parents make him a Jew or a Christian."
Shows people are born pure, not guilty.
Where the ruling is recorded
- al-Fiqh al-Akbar (Imam Abu Hanifa), Section on Allah's creation of people and their faith. States that Allah created people free of belief and disbelief, then addressed them, and each chose.
- Tafsir Ibn Kathir, Commentary on Surah al-Baqarah, the story of Adam. Explains Adam's repentance and its acceptance.
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.