Yes, at least publicly and legally. At least up until the 90's (and I don't suppose it's changed under the prolonged recession but I'm not sure,) women could not take out a mortgages. A few women got together and started a bank (with a pink ribbon logo) to do just this, but they had to have a male CEO and the bank closed rather too quickly. We have very few MPs, ministers or CEO's. It is hard to get accolade for any work other than "women's work", which would be nursing, and perhaps early childhood education. Even top chefs, top weavers, and heads of flower arrangement and tea ceremony schools are almost all men.
The very word "nurse" ("kango-fu"), although a description of profession, denotes woman (the suffix "fu"), in the same way fireman, postman and chairman denotes men, though I realize in the English language it also means "human".
In the early 90's when it became evident we needed more men in nursing, particularly geriatric nurses, (and this happened around the time I left Japan, so my knowledge is admittedly murky, but,) they established a different qualification based on a different training scheme and named it "kango-shi", a man ("shi"), in the same vein as fireman ("sh0h-b0h-shi") or pharmacist ("yakuzai-shi", nothing to do with Yakuza, mind,) but not doctor ("i-shi"; here "shi" means teacher; the Japanese language has homophones by the truck loads.)
In the language's defense, we also have many, many gender neutral professions, driver ("unten-shu", hand, ) MC ("shikai-sha", person), shop-owner ("insert-item-ya", shop, including postmen who delivers, "yubin-ya") or chairman ("shuseki", chair). There was some kind of an equal employment opportunity law passed possibly in the bubbly 80's, but a) employers can specify skills that eliminate all but the most gun-ho women from trying, and b) there are still tons of want ads for "pretty ladies between the ages of 18 and 24 looking for an easy way to earn high salary" and the like.
I hasten to add, I don't think many Japanese women think about this much, and when they do, they may not be bothered, because "segregation/separation" has its merits. Japanese gender specific responsibilities can certainly makes life easier for women; women are seldom expected to lift heavy stuff in a supermarket but just mind the till. Though, again, at least until the early 90's.
Literature, from diaries, poems (poet, "shijin") to novels (novelist "sakka"), the playing field have been comparatively level, though I have heard female authors complain publishers sometimes ask to sleep with them if they want to be published. And even the best of them sometimes can't escape being prefixed "women", ("jyoryuh-sakka", "jyoryuh-shijin").
Sometimes this is why women give up hitting their heads on the not-so-transparent glass ceiling and decide to marry belatedly. (But not in my case; well, not strictly.)
But fret not. Inside the home, women often have a lot of power. For example in many homes wives/women have total control of the money, often even the larger purchases, and the children's education. That is why the wife is sometimes called "Yama-no-Kami", God (not Goddess) of the Mountain!
PS: Back in the 70's, I thought replacing "man" with "one" was shorter and smarter than "person", i.e. "fire-one", "mail-one" and "chair-one" to match the use of "one" as in "one does not flaunt one's success," but nearly 40 years later, they sounds superbly comical, don't they!