Since she does not need to pray she should only enter if there is a good reason like attending a class that cannot be found elsewhere. The masjid is defined as the usual prayer area that has been designated for the five daily prayers (not the overflow areas).
What the Scholars Said
It is not allowed according to the four mainstream schools of thought.
It is only allowed if she made wudu and can ensure that nothing soils the masjid: Ahmad ibn Hanbal (in one narration) [Al-Isnsaf 1:347]
It is allowed according to: 1) Ahmad ibn Hanbal (in one narration) [Al-Isnsaf 1:347] 2) Muzani (the student of ash-Shafii) [Al-Isnsaf 1:347] 3) Ibn Hazm [Al-Isnsaf 1:347]
Since the overwhelming majority of scholars said it is prohibited, although it is based on a weak hadith, it should only be done when there is a good reason such as attending a class that cannot be found elsewhere.
Shaykh Mustafa Umar