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

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

Al-Bukhaari (2026) and Muslim (1172) narrated from ‘Aa’ishah (may Allaah be pleased with her), the wife of the Prophet (peace and blessings of Allaah be upon him), that the Prophet (peace and blessings of Allaah be upon him) used to spend the last ten nights of Ramadaan in i'tikaaf until he passed away, then his wives observed i'tikaaf after he died. 

It says in ‘Awn al-Ma’bood: 

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

Shaykh ‘Abd al-‘Azeez ibn Baaz (may Allaah have mercy on him) said: 

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

From the internet website of Shaykh Ibn Baaz. 

And Allaah knows best.