Muslims vary in their understanding of Islam and the Qur'an, as well as in their customs (which they often support in the name of religion).
Feminism is also a very broad concept encompassing many things, some of which might be in harmony with the ethos of the Qur'an and others which may not. (So, basically, one can't evaluate feminism as a whole; rather, one has to look at specific ideas.)
Therefore, there isn't a single answer to this. However, there are generally 3 approaches:
* A heavily patriarchal approach, which gives men a lot of dominance and a central position, and sees women primarily in terms of how they relate to men.
* The idea that women and men are spiritually equal but that in the material realm, men have dominance, leadership roles, or superiority in some ways.
* Women and men are equal, and/or that Islam liberates women from having to define their worth on the basis of how attractive or useful they are to men.
Seeing as so many people give many views on this question in this day and age, I don't think it's appropriate for me to impose my own view, but you can read the Qur'an, and consider what people say about Islam, in light of those paradigms and see which it seems to fit. There is also a lot written these days on the subject of Islam and gender which can be pondered.
However, I do think that the best way to approach this question as a believer is to view it from the angle of "what is the will of the creator of the universe?" This sometimes helps keep the subject focused and away from emotional assumptions, pseudo-science, or minutiae that sometimes creep into these discussions.
Personally, I also tend to be cautious of getting too focused on any sort of -ism, because an -ism is a human-made ideology and therefore has limitations, whereas Allah is unlimited. Of course this doesn't mean that we shouldn't discuss -isms, incudng feminism; however, in my view, the question should be "is feminism an island that can fit into the ocean of Islam" not "does Islam fit into feminism".