Praise be to Allah.
I’tikaaf is only valid if done 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”
Men and women are equal in this regard.
Ibn Qudaamah said in al-Mughni:
A woman has the right to observe i‘tikaaf in any mosque, and that is not subject to the condition that it be a mosque where prayers are performed in congregation, because that is not obligatory upon her. This was the view of al-Shaafa’i.
She does not have the right to observe i'tikaaf in her house, because Allaah says “while you are in I‘tikaaf (i.e. confining oneself in a mosque for prayers and invocations leaving the worldly activities) in the mosques”, and because 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.
Al-Nawawi said in al-Majmoo’ (6/480):
It is not correct for a man or a woman to observe i'tikaaf anywhere except in the mosque.
This is the view favoured by Shaykh Ibn ‘Uthaymeen in al-Sharh al-Mumti’, 6/513
And Allaah knows best.