Page 538 of the shariah manual “Reliance of the Traveller“ states that a woman needs permission from her husband to leave the house.
The Quran prescribes that a woman should preferably stay at home unless she has a good reason. Going to work to earn money is not a good reason as this is the exclusive duty of her husband or father.
While verse 33.33 was revealed concerning the wives of Muhammad, there are a number of Hadith that indicate that women need the permission of their husbands to leave the house.
33.33. And stay quietly in your houses, and make not a dazzling display, like that of the former Times of Ignorance; and establish regular Prayer, and give regular Charity; and obey Allah and His Messenger. And Allah only wishes to remove all abomination from you, ye members of the Family, and to make you pure and spotless.
One of the Hadith that indicates that women need to have their husband’s permission to leave the house is the following:
Narrated Salim's father: The Prophet said, "If the wife of anyone of you asks permission to go to the mosque, he should not forbid her."
In this instance, Mohammed gives a permission for a specific activity, namely going to the mosque. She has to ask permission and her husband has to let her go.
It becomes more funny when Mohammed issued a permission to let women go to the toilet outside of the house, apparently without permission of the husband. Please note that Mohammed needed “divine inspiration” to issue this ruling. So permission for women to leave the house seemed not to be evident.
Narrated 'Aisha: Once Sada bint Zam'a went out at night for some need, and 'Umar saw her, and recognizing her, he said (to her), "By Allah, O Sada! You cannot hide yourself from us." So she returned to the Prophet and mentioned that to him while he was sitting in my dwelling taking his supper and holding a bone covered with meat in his hand. Then the Divine Inspiration was revealed to him and when that state was over, he (the Prophet was saying: "O women! You have been allowed by Allah to go out for your needs."
The wording “for some need” is illustrated in the Hadith of Bukhari 1.4.148 in which it is described as “answering the call of nature” which means going to the toilet.
In the islamic way of thinking, the fact that a woman needs her husband’s permission is very logic. The husband is responsible for his wife and if she is allowed to go wherever she wants without him knowing her whereabouts, he can not perform his duty of assuring her safety and moral integrity. This is also the reason why women are not allowed to drive in Saudi-Arabia. The Saudi government wants to protect women against the dangers of being alone on the road and potentially being exposed to indecent men, for example when their car breaks down on a road in the desert.
If she does leave the house or travel without his permission, islamic law states (m11.9 (2) on page 545) that he does not have to provide maintenance for her during those days.