Praise be to Allah.
What is prescribed in the event of a solar or lunar eclipse is for the Muslim to turn to Allah in prayer, remembering Him, calling upon Him and asking Him for forgiveness, and to give charity and do other righteous deeds.
It was narrated that Abu Mas‘ood al-Ansaari (may Allah be pleased with him) said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “The sun and the moon are two of the signs of Allah by means of which Allah creates fear in His slaves. They do not become eclipsed for the death of any person. If you see anything happen to them, then pray and call upon Allah until you are relieved of that.”
Al-Bukhaari (1059) and Muslim (912) narrated that Abu Moosa (may Allah be pleased with him) said: The sun was eclipsed, and the Prophet (blessings and peace of Allah be upon him) got up in a state of anxiety, thinking that it was the Hour. He came to the mosque and began to pray, standing, bowing and prostrating for the longest time I ever saw him do, and he said: “These signs that are sent do not occur for the death or birth of anyone, rather Allah sends them to create fear in His slaves. If you see any of them, then hasten to remember Him, call upon Him and ask Him for forgiveness.”
Ibn Battaal said: The words “If you see any of them [these signs], then hasten to remember Him, call upon Him and ask Him for forgiveness” were narrated by al-Bukhaari in Baab adh-Dhikr fi’l-Kusoof (Remembering Allah at the time of an eclipse). He said: The Messenger of Allah (blessings and peace of Allah be upon him) instructed us to call upon Allah when they (eclipses) occur, and to seek forgiveness, as he also instructed us to pray.
This indicates that it is not narrated from them (the Sahaabah) that when an eclipse occurred, they were encouraged to pray only; rather they were encouraged to do deeds by means of which they could draw close to Allah, such as praying, calling upon Allah (du‘aa’), seeking His forgiveness (istighfaar) and so on."(Sharh Saheeh al-Bukhaari by Ibn Battaal 3/32)
In this regard a woman is like a man, because of the general meaning of the texts. So in her case the same is prescribed for her as is prescribed for a man, namely praying, calling upon Allah, seeking His forgiveness, giving charity, and so on.
If a woman has any impediment that prevents her from praying, then in this situation she can still do other things: calling upon Allah, giving charity, seeking Allah’s forgiveness, remembering Him, and other deeds by means of which she may draw close to Allah.
For more information, please see the answer to question no. 26753.
And Allah knows best.