Fatwa of Ayatullah Sistani -great Marja' of Najaf- regarding your question,
Based on obligatory precaution, it is not permissible for them [i.e., non-Muslims] to enter the mosque(masjid). As for their entering the places of worship, etc(e.g., the shrine of Imams), there is no problem in it. If their entry [in shrine of Imams or a husayniyya or a center] without hijãb is considered as a sign of disrespect, hijãb should be enforced on the [non-Muslim] women. Source, Question 2