The scholars are agreed that a man’s i’tikaaf is only valid if observed in the mosque, because Allaah says (interpretation of the meaning): 

“And do not have sexual relations with them (your wives) while you are in I‘tikaaf (i.e. confining oneself in a mosque for prayers and invocations leaving the worldly activities) in the mosques”

[al-Baqarah 2:187]

So i’tikaaf is something that should be done specifically in the mosque. 

See al-Mughni, 4/461 

With regard to women, the majority of scholars are of the view that as in the case of men, their i’tikaaf is not valid unless it is observed in the mosque, because of the verse quoted above (interpretation of the meaning): 

“And do not have sexual relations with them (your wives) while you are in I‘tikaaf (i.e. confining oneself in a mosque for prayers and invocations leaving the worldly activities) in the mosques”

[al-Baqarah 2:187]

The wives of the Prophet (peace and blessings of Allaah be upon him) asked him for permission to observe i’tikaaf in the mosque and he gave them permission, and they used to observe i’tikaaf in the mosque after he died. 

If it were permissible for a woman to observe i’tikaaf in her house, the Prophet (peace and blessings of Allaah be upon him) would have told them to do that, because it is better for a woman to remain concealed in her house than to go out to the mosque. 

Some of the scholars were of the view that it is valid for a woman to observe i’tikaaf in the “mosque” of her house, which is the place that she allocates for prayer in her house. 

But the majority of scholars said that this is not allowed and said that the place where she prays in her house is not called a masjid (mosque) except by way of metaphor, and it is not really a mosque, so it does not come under the rulings on mosques, hence it is permissible for people who are junub and menstruating women to enter it. 

See al-Mughni, 4/464. 

Al-Nawawi said in al-Majmoo’ (6/505): 

It is not valid for men or women to observe i’tikaaf anywhere but in the mosque; it is not valid in the mosque of a woman’s house or the mosque of a man’s house, which is a space that is set aside for prayer. 

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) was asked in Majmoo’ al-Fataawa (20/264) about where a woman who wants to observe i’tikaaf should do so? 

He replied: 

If a woman wants to observe i’tikaaf, she should observe i’tikaaf in the mosque so long as that does not involve anything that is forbidden according to sharee’ah. If that does involve anything that is forbidden then she should not do i’tikaaf. 

In al-Mawsoo’ah al-Fiqhiyyah (5/212) it says: 

The scholars differed as to where women should observe i’tikaaf. The majority are of the view that woman are like men, and their i’tikaaf is not valid unless observed in the mosque. Based on this it is not valid for a woman to observe i'tikaaf in the mosque of her house, because of the report narrated from Ibn ‘Abbaas (may Allaah be pleased with him) who asked about a woman who vowed to observe i’tikaaf in the mosque of her house. He said: “(This is) an innovation, and the most hateful of actions to Allaah are innovations (bid’ah).” So there can be no i’tikaaf except in a mosque in which prayers are established. And the mosque of a house is not a mosque in the real sense of the word and does not come under the same rulings; it is permissible to change it, and for a person who is junub to sleep in it. Moreover if it were permissible (to observe i’tikaaf at home), the Prophet’s wives (may Allaah be pleased with them) would have done that at least once to show that it is permissible.