Women do not customarily cover their heads in order to arouse fear of heaven within themselves. As a matter of tzni’ut, married women must cover their hair, but single women, who are not required to cover their hair for reasons of tzni’ut, do not normally walk around in a head covering like men. Perhaps the reason that women do not need a yarmulke is that they naturally find it easier to improve themselves. Men are perhaps bolder, and therefore they need yarmulkes on their heads to restrain and focus that trait. Women, who by nature are more reserved and more modest, have no such need.
Another possible explanation is that by observing the laws of tzni’ut in the way they dress, women more clearly convey acceptance of the yoke of heaven upon herself and therefore do not require a head covering to express their fear of God. In contrast, even if a woman who does not abide by the rules of modesty were to wear a yarmulke, it would be to no effect, for her transgression of the laws of tzni’ut is very severe; by neglecting to observe the halakhot which pertain to her, it is as if she is declaring that she is not bound by halakha, the word of God.
There are, however, poskim who maintain that single women, too, must cover their heads when reciting God’s name and saying berakhot. They maintain that in this matter there is no distinction between men and women; rather the command to cover one’s head when mentioning God’s name is a separate obligation (Ish Matzli’aĥ, Yaskil Avdi). Others say that at the very least, women must cover their heads while reciting the Amida (Yabi’a Omer 6:15). However, in practice, single women are not strict concerning this, and even while praying the Amida they do not normally cover their heads. The reason for this is that men have adopted the pious custom of covering their heads all day in order to inspire their fear of God. Therefore, there is ample reason to require them to wear a head covering when mentioning God’s name. But for single women, who do not practice this custom, a head covering does not demonstrate fear of God, and hence they are not obligated to wear one while praying and reciting berakhot.
Nonetheless, married women certainly must cover their hair for prayer, since without a hair covering they are not dressed in accordance with the laws of tzni’ut; certainly if they were to pray in that manner it would be disrespectful. One must come to prayer in distinguished clothing, befitting someone who stands before the King of the universe, so certainly one must properly observe the halakhot of modest attire. Therefore, even women who do not abide by the law and do not normally cover their hair should cover it while praying.
When mentioning God’s name, some poskim say that married women must be strict about head-covering, even in complete privacy. Others say that since single women are not obligated to do so, married women are not obligated either. The rationale is that the obligation of married women to cover their hair is a function of tzni’ut alone, and since there is no obligation to dress in a respectable fashion when reciting berakhot, there is no reason to distinguish between married and unmarried women, so married women may recite berakhot and Shema without a hair covering. 1
- Responsa Ish Matzli’ach OĤ 24-25, and Yaskil Avdi vol. 7, p. 289 state that single women must cover their heads when reciting berakhot. Yabi’a Omer 6:15 provides a comprehensive summary of the issue and concludes that single women should not be prevented from reciting a berakha bareheaded; however, it is proper for them to cover their heads while praying the Amida, as Rambam says. Married women, even when reciting a berakha, must cover their heads, as indicated in Ĥesed La-alafim 2:8.
However, the widespread custom is that single women pray, whether at home or in the synagogue, without a head covering. The rationale behind Rambam’s ruling that a head covering is necessary when praying is that by covering one’s head, one expresses his or her fear of God, and therefore certainly this is how one must pray the Amida. Yet, for single women, the yarmulke does not symbolize fear of God, and hence they may pray bareheaded. Tzitz Eliezer 12:13 reinforces the practice of praying pare-headed with the reason offered by Ĥatam Sofer: since gentile women customarily cover their heads in their houses of worship, Jewish women should be careful not to imitate that custom.
Nevertheless, if a married woman, who must cover her hair for reasons of tzni’ut, stands in prayer while not dressed in keeping with the mandatory parameters of tzni’ut in front of others, it certainly constitutes an affront to the honor of Heaven.
Reciting berakhot is not considered to be standing before the King, so a woman in private, when the laws of tzni’ut do not require her to cover her hair, there is no need for her to cover her head while reciting a berakha. However, Yabi’a Omer 6:15 and Halikhot Bat Yisrael 5:3 state that married women must cover their heads when mentioning God’s name, even when in complete privacy. Still, in practice, many married women normally recite the bedtime Shema and Ha-mapil without a head covering. It seems that the reason for this is what I wrote above, that the obligation to wear a yarmulke when reciting berakhot is based on the pious custom to cover one’s head throughout the entire day. Since the yarmulke inspires fear of God all day, it follows that one must also wear it while invoking God’s name. However, women, who do not customarily wear a yarmulke to inspire fear of God, need not wear one when mentioning God’s name either. There is proof for this in m. Ĥalla 23: “A woman may sit and separate the ĥalla while nude.” Nude here obviously means bareheaded, for it would not make sense that she is required to cover her head but allowed to recite the berakha while nude. R. Shlomo Zalman Auerbach rules this way too, saying that women’s custom to cover their heads in the mikveh while making the berakha on immersion does not obligate them in this practice for all other berakhot (Halikhot Bat Yisrael 5 n. 6). Therefore, a woman who wakes up in the middle of the night to relieve herself is not obligated to cover her head while reciting Asher Yatzar. Likewise, a woman who walks around her house bareheaded (when there are no strangers around) and wants to drink something is allowed to recite She-hakol and Borei Nefashot without a head-covering.
Source: http://ph.yhb.org.il/en/02-10-06/