A woman can perform itikaaf but only in the mosque
Regarding women, the public scholars say that like men, women's I'tikaf is not valid in any place other than the mosque, the proof of this is the following verse:
{And do not have intercourse with women when you are in the state of I'tikaf in the mosque} Al-Baqarah (187).
And also because
The pure wives of the Prophet (may God bless him and grant him peace) asked the Prophet (may God bless him and grant him peace) for permission to perform itikaaf in the mosque, and the Prophet (may God bless him and grant him peace) gave them permission.
And even after the death of the Prophet (peace be upon him), she used to perform itikaaf in the mosque.
And if it was permissible for a woman to perform I'tikaf in her own home, the Prophet (peace and blessings of Allah be upon him) would have guided her because her veil is more than going to the mosque in her own home, yet he allowed I'tikaf in the mosque itself.
Some scholars say:
A woman can perform I'tikaf at her place of prayer at home, but the popular scholars forbid her to do so, saying:
The place of prayer in his house cannot be called a mosque, but it can only be called a mosque in virtual terms, and in reality it cannot be called a mosque.
That is why its rules will not be those of the mosque, that is why a male and a menstruating woman can enter the prayer place at home.
See al-Mughni Laban Qudama al-Maqdisi (4/464).
Imam Nawi, may God have mercy on him, says in his book "Al-Majmoo":
Itikaf of men and women without a mosque is not valid.
It is not right for a woman to perform I'tikaf in the mosque of her home, nor for a man to perform I'tikaf in his house at the place of prayer.
That is, the place which is prepared for prayer in a corner of the house is called the house mosque.
See al-Majmoo (6/505).
Shaykh Ibn Uthaymeen (may God have mercy on him) was asked the following question:
If a woman wants to do Itikaaf, where will she do Itikaaf?
The answer of Toshikh (may Allah have mercy on him) was:
When a woman wants to perform I'tikaf, if there is no Shariah in it, she will perform I'tikaf in the mosque, and if there is any Shariah in it, then the woman will not perform I'tikaf. Ah
See the collection of al-Fatawi Ibn Uthaymeen (may God have mercy on him) (20/264).
And in al-Musawiyyah al-Fiqhiyyah it is said:
There is a difference of opinion regarding the place of I'tikaf for a woman. The public scholars used to describe it as the same as a man and say that it is not valid for a woman to I'tikaf anywhere except the mosque. in :
When Ibn Abbas, may God be pleased with him, was asked about a woman's I'tikaf in the mosque of her house, he said:
It is an innovation for a woman to perform I'tikaf at home, and the most abhorrent actions to Allah are innovations, therefore I'tikaf is not valid anywhere except in a mosque with congregational prayer, because the place where prayer is held at home is neither really a mosque, nor is it permissible to change it and change it. It is also permissible to sleep with a person on the other side, and if it were permissible, the mothers of the believers would have practiced it first, even though they would have done it twice to justify it.
See Al-Musua'at al-Fiqhiyyah (5/212).
God knows.