Praise be to Allah.
What is required by this woman if her husband dies is to observe an ‘iddah of four months and ten days, because she comes under the general meaning of the verse in which Allah says (interpretation of the meaning):
“And those of you who die and leave wives behind them, they (the wives) shall wait (as regards their marriage) for four months and ten days”
In the event of divorce, she must observe an ‘iddah of three months, because she does not menstruate. That is because of the general meaning of the verse in which Allah says (interpretation of the meaning):
“And those of your women as have passed the age of monthly courses, for them the Iddah (prescribed period), if you have doubts (about their periods), is three months, and for those who have no courses ((i.e. they are still immature) their Iddah (prescribed period) is three months likewise, except in case of death)”
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: If she has ceased menstruating for some reason and she knows that her menses will not resume, such as if her uterus has been removed, she comes under the same heading as one who has passed the age of monthly courses (i.e., post-menopause), so she should observe an ‘iddah of three months.
End quote from Fataawa Islamiyyah, 3/311
Although removal of the uterus means that we may be certain that she is not pregnant, it does not mean that observing the ‘iddah is not obligatory in her case, because the wisdom behind the ‘iddah is not limited to ascertaining that there is no pregnancy.
Ibn al-Qayyim (may Allah have mercy on him) said in I‘laam al-Muwaqqa‘een (2/51): The purpose of the ‘iddah is not only to ascertain that there is no pregnancy; rather that is only one of its aims and wisdoms. End quote.
He also mentioned some of these wisdoms in the same book (2/50, 51) where he said: There are a number of reasons behind the prescription of the ‘iddah, one of which is to ascertain that there is no pregnancy, so that the water (semen) of two or more men will not be present in one womb, lest lineages become mixed, leading to negative consequences that are prohibited by sharee‘ah and wisdom. One of these aims is to highlight the importance of this contract (marriage contract) and show how great and honourable it is. Another is to give a lengthy period of time in which a man who has divorced his wife may take her back, because he may regret it and decide to take her back, so he will have enough time to so. Another purpose is to fulfil the rights of the husband (in the event of his death) and highlight the impact of his loss in the prohibition on adorning herself. Hence the prescribed period of mourning for the husband is longer than that for a parent to a child. Another purpose is to protect the rights of the husband and the interests of the wife, the rights of the child and the rights of Allah that He has enjoined. There are four rights that are acknowledged in the ‘iddah. End quote.
And Allah knows best.