I’tikaf of women in the Mosque

Yes, it is permissible for a woman to observe i’tikaf in the mosque during the last ten days of Ramadan. 

Indeed, i'tikaf is Sunnah for both men and women, and the Mothers of the Believers (may Allah be pleased with them [i.e., the wives of the Prophet (peace and blessings of Allah be upon him)] used to observe i’tikaf with the Prophet (peace and blessings of Allah be upon him) during his lifetime, and after he passed away.   

Al-Bukhari (2026) and Muslim (1172) narrated from ‘Aishah (may Allah be pleased with her), the wife of the Prophet (peace and blessings of Allah be upon him), that the Prophet (peace and blessings of Allah be upon him) used to spend the last ten nights of Ramadan in i'tikaf until he passed away, then his wives observed i'tikaf after he died. 

It says in ‘Awn al-Ma'bud: 

“This indicates that women are the same as men when it comes to i'tikaf .” 

Shaykh ‘Abd al-‘Aziz ibn Baz (may Allah have mercy on him) said: 

"I’tikaf is Sunnah for both men and women, because it was proven that the Prophet (peace and blessings of Allah be upon him) used to observe i'tikaf during Ramadan, and finally he settled on i'tikaf during the last ten days, and some of his wives used to observe i'tikaf with him, then they observed i’tikaf after he died. The place for i'tikaf is the mosque in which prayers in congregation are performed." 

For more about women’s i’tikaf, please see these answers: 37911 and 50025

And Allah knows best.