Question: Is it permissible for a woman to perform i’tikaaf at the place of prayer in her home?
Response: No. If a woman wishes to perform i’tikaaf, then she should do so in a masjid, so long as there is no danger in that (such as free-mixing and complacency regarding the hijaab, etc). (However), if there is any danger in that, then she should not perform i’tikaaf.
Shaykh Ibn ‘Uthaymeen
Fataawa Ramadhaan – Volume 2, Page 891, Fatwa No.877
Fiqh al-‘Ibaadaat – Page 209.fatwaonline.com