The Shulhan Aruch (Orah Hayim 186) rules that the obligation to recite Birkat Hamazon after eating bread applies to both men and women. He then adds, however, that the nature of a woman’s obligation to recite Birkat Hamazon is uncertain. The Gemara records a debate as to whether women are required to recite Birkat Hamazon on the level of Torah obligation, like men, or on the level of Rabbinic enactment. As the Mishna Berura explains, this distinction, which is drawn by one view in the Gemara, stems from two factors. First, when the Torah introduces the obligation of Birkat Hamazon, it describes it as a blessing recited "over the good land that He has given you" (Debarim 8:10), referring to the Land of Israel. When Beneh Yisrael entered the Land, its territory was divided among the men, and not the women. For this reason, one view contends that the Torah obligation of Birkat Hamazon – which relates to the Land of Israel – does not apply to women. Secondly, the text of Birkat Hamazon makes mention of Berit Mila – which obviously does not apply to women – and also Torah learning, a Misva that does not apply to women as it applies to men. This, too, might be a reason to exclude women from the Torah obligation of Birkat Hamazon. Thus, according to one view in the Gemara, women are obligated to recite Birkat Hamazon only by force of Rabbinic enactment, and not by force of Torah obligation.
As this question was not definitively resolved, the Shulhan Aruch writes that it remains uncertain whether or not women are obligated in Birkat Hamazon on the level of Torah obligation.
The practical implication of this question relates to a situation where a woman cannot remember whether or not she recited Birkat Hamazon. It sometimes happens that because of her preoccupation with serving and clearing, a woman does not remember whether or not she recited Birkat Hamazon after a meal. If this happens to a man, he must certainly recite Birkat Hamazon. Halacha requires one to follow the stringent possibility in situations of uncertainty regarding a Torah obligation, and thus with regard to the Torah obligation of Birkat Hamazon, one must assume that he did not fulfill the Misva and recite Birkat Hamazon. In the case of a woman, however, if her obligation applies only on the level of Rabbinic enactment, then she would not recite Birkat Hamazon in situations of doubt, as Halacha allows assuming the lenient possibility with regard to Rabbinic obligations.
In light of this question, a woman who cannot remember whether or not she recited Birkat Hamazon should not recite it. Since her obligation may apply only on the level of Rabbinic enactment, it is questionable whether she should recite Birkat Hamazon in situations of uncertainty, and we therefore apply the famous rule of "Safek Berachot Le’hakel" – one does not recite a Beracha whose obligation is subject to doubt.
Another ramification of this issue is a case where a husband wishes to fulfill the Misva of Birkat Hamazon by listening to his wife’s recitation, rather than recite it himself. If both ate a full meal with bread, and the husband, for whatever reason, prefers not to personally recite Birkat Hamazon, he may want his wife to recite it for him. However, since women might bear a lower level of obligation in this Misva than men, a man should recite Birkat Hamazon personally rather than listen to its recitation from a woman. One cannot fulfill an obligation to recite a certain text by listening to its recitation by somebody who bears a lower level of obligation. Therefore, a man may not fulfill the obligation of Birkat Hamazon by listening to its recitation by a woman. The exception to this rule is a situation where a man ate only a Ke’zayit of bread, in which case his obligation, too, applies on the level of Rabbinic enactment. In such a case, then, if the man is unable to recite Birkat Hamazon, he can have a woman recite the text for him, since he does not have a higher level of obligation.
Summary: Women are obligated in Birkat Hamazon, but if a woman is uncertain whether or not she recited Birkat Hamazon after a meal, she should not recite it. A man who does not wish to personally recite Birkat Hamazon should not have a woman recite it for him, unless he did not eat more than a Kezayit of bread.
