I’tikaf for Females: At Home or in the Mosque?
Question

Can a woman observe i’tikaf in her house?
Praise be to Allah.The scholars are agreed that a man’s i’tikaf is only valid if observed in the mosque, because Allah says (interpretation of the meaning): 
“And do not have sexual relations with them (your wives) while you are in I‘tikaf (i.e. confining oneself in a mosque for prayers and invocations leaving the worldly activities) in the mosques.” [al-Baqarah 2:187]
So i'tikaf 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’tikaf 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‘tikaf (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 Allah be upon him) asked him for permission to observe i’tikaf in the mosque and he gave them permission, and they used to observe i’tikaf in the mosque after he died. 
If it were permissible for a woman to observe i’tikaf in her house , the Prophet (peace and blessings of Allah 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’tikaf 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-Majmu’ (6/505): 
“It is not valid for men or women to observe i’tikaf 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 ‘Uthaymin (may Allah have mercy on him) was asked in Majmu’ al-Fatawa (20/264) about where a woman who wants to observe i’tikaf should do so? 
He replied: 
“If a woman wants to observe i’tikaf, she should observe i’tikaf in the mosque so long as that does not involve anything that is forbidden according to shari’ah. If that does involve anything that is forbidden then she should not do i’tikaf.” 
In al-Mawsu’ah al-Fiqhiyyah (5/212) it says: 
“The scholars differed as to where women should observe i’tikaf. The majority are of the view that women are like men, and their i’tikaf is not valid unless observed in the mosque. Based on this it is not valid for a woman to observe i'tikaf in the mosque of her house, because of the report narrated from Ibn 'Abbas (may Allah be pleased with him) who asked about a woman who vowed to observe i’tikaf in the mosque of her house. He said: “(This is) an innovation, and the most hateful of actions to Allah are innovations (bid’ah).” So there can be no i'tikaf 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’tikaf at home), the Prophet’s wives (may Allah be pleased with them) would have done that at least once to show that it is permissible.”