Praise be to Allah.
It is possible to divide the types of antiperspirant – in terms of ruling on a woman using them – into two categories:
The first category is antiperspirants that are scented with a discernible fragrance. It is not permissible for a woman to use this type outside the house, if she thinks it most likely that she will walk past some men and they will smell the fragrance.
The evidence for that is the hadith of Zaynab, the wife of ‘Abdullah (may Allah be pleased with them both), who said: The Messenger of Allah (blessings and peace of Allah be upon him) said to us: “When one of you comes to the mosque, let her not put on any perfume.” Narrated by Muslim (443).
As he (blessings and peace of Allah be upon him) forbade women to go out to the mosque wearing perfume, because it was most likely that men would notice the fragrance because the place was small and there was no barrier between the men and women, then it is more appropriate that a woman who is going out to the marketplace and other places where people gather should not be allowed to use perfume.
There are other hadiths which speak of that, some of which have been quoted previously in the answer to question no. 102329 .
The second category is unscented antiperspirants, or those that have a light fragrance that is not obvious and does not go beyond the user. There is nothing wrong with a woman using this type, and there is no reason to disallow it.
Ar-Ramli ash-Shaafa‘i (may Allah have mercy on him) said:
In the case of a woman, it is not allowed for her to put on perfume and wear adornment and fancy clothes when she wants to attend [the mosque]. In fact, it is appropriate for her to rid herself of unpleasant odours. End quote .
Ash-Shabraamalsi commented on these words, saying: “In fact, it is appropriate for her to rid herself of unpleasant odours” means: Even if what is used to remove unpleasant odours has a fragrance, as this is the only way to achieve that result – but is on condition that men cannot smell that fragrance. End quote from Nihaayat al-Muhtaaj (2/340).
But if the woman thinks it most likely that she will not pass any men; rather she will be among other women like her, in that case there is nothing wrong with her using perfume or antiperspirant.
And Allah knows best.