Short answer
Not by simply refusing it. Your share becomes yours by Allah's ruling the moment the person dies, and saying "I give it up" does not remove it in the Hanafi school. But once you own it, an adult heir can gift it to others, or agree with the other heirs to take something else in exchange for it.
Inheritance passes into the heir's ownership by force of law, without any acceptance. An adult, sane heir may then gift the share with handing over, or settle with the other heirs by takharuj (withdrawal for an agreed exchange). A minor's share cannot be given up, even by a guardian.
The four schools agree on this.
Explanation
People ask this for many reasons: a sister who wants to help her brothers, a son who wants his mother to have more, or someone who wants nothing to do with a difficult estate. Islam allows generosity, but through the right steps.
Why you cannot just refuse. Allah calls the shares an obligatory portion. When someone dies, each heir's share passes to them automatically. Hanafi jurists state that if an heir says "I have left my right", the right is not lost, because ownership does not end by leaving it.
- Gift your share once the estate is worked out. Say clearly what you are giving and to whom, and hand it over. In Hanafi law a gift is complete only with possession.
- Takharuj (settlement). The heirs agree that you withdraw from the estate in return for a specific item or sum, and the rest is divided among the others.
- Use your local legal process, such as a deed of variation in the UK or a disclaimer in the US, and make sure the legal result matches what you intend Islamically.
- No one may pressure a woman, or anyone, into giving up her share. This happens in some cultures and is a serious wrong.
- A child's share cannot be given away at all.
- Give from conviction, not from shame or family pressure.
Every estate is different, so ask a mufti before you sign anything. See who inherits and the inheritance calculator.
Ask a mufti about your own case. This answer explains the general ruling. When the details of your situation matter, as they do here, ask a qualified mufti and give them the full facts. Where to ask a scholar.
The evidence
Quran, Surah An-Nisaa 4:7
لِّلرِّجَالِ نَصِيبٌۭ مِّمَّا تَرَكَ ٱلْوَٰلِدَانِ وَٱلْأَقْرَبُونَ وَلِلنِّسَآءِ نَصِيبٌۭ مِّمَّا تَرَكَ ٱلْوَٰلِدَانِ وَٱلْأَقْرَبُونَ مِمَّا قَلَّ مِنْهُ أَوْ كَثُرَ ۚ نَصِيبًۭا مَّفْرُوضًۭا ﴿٧﴾
For men is a share of what the parents and close relatives leave, and for women is a share of what the parents and close relatives leave, be it little or much - an obligatory share.
The shares are fixed by Allah and pass to the heirs by right.
Quran, Surah An-Nisaa 4:29
يَٰٓأَيُّهَا ٱلَّذِينَ ءَامَنُوا۟ لَا تَأْكُلُوٓا۟ أَمْوَٰلَكُم بَيْنَكُم بِٱلْبَٰطِلِ إِلَّآ أَن تَكُونَ تِجَٰرَةً عَن تَرَاضٍۢ مِّنكُمْ ۚ وَلَا تَقْتُلُوٓا۟ أَنفُسَكُمْ ۚ إِنَّ ٱللَّهَ كَانَ بِكُمْ رَحِيمًۭا ﴿٢٩﴾
O you who have believed, do not consume one another's wealth unjustly but only [in lawful] business by mutual consent. And do not kill yourselves [or one another]. Indeed, Allah is to you ever Merciful.
Giving up a share must be by free consent, never pressure.
Sahih al-Bukhari 6732
Sahih... ألحقوا الفرائض بأهلها فما بقي فهو لأولى رجل ذكر ...
"Give the fixed shares to those entitled to them, and what remains goes to the nearest male relative."
Shares are set by the sharia, not chosen by the heirs.
Where the ruling is recorded
- al-Ashbah wa al-Naza'ir (Ibn Nujaym), Section on rights that can and cannot be waived. An heir who says he has left his right still owns his share.
- al-Hidaya, Kitab al-Sulh, section on takharuj. Settlement among heirs for an agreed exchange.
- Radd al-Muhtar (Ibn Abidin), Kitab al-Hiba. A gift is complete with possession; a guardian cannot gift a minor's property.
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.