This Shabbat, the Shabbat before Purim, we read Parshat Zachor from Dvarim 25:17-19, “Remember what Amalek perpetrated against you on the way when you were going out of Egypt…do not forget.”
According to Sefer HaChinuch, Mitzvah 603, women are exempt from the mitzvah of Zachor and do not need to listen to Parshat Zachor: “This mitzvah applies only to men and not to women since men and not women must wage war and take vengeance from the enemy.”
In Rambam’s Sefer HaMitzvot, Positive Mitzvah 189, there is no specific exemption for women from Parshat Zachor, which leads us to believe that women are obligated.
The Minchat Chinuch teaches that the mitzvah of Zachor, “remember” is not a positive precept dependent on time (especially since it also includes the negative commandment to “not forget”) and therefore women are not exempt. As well, in an obligatory war, all go out to fight including a bride from her bridal chamber (Mishna Sotah 8). Therefore all Israelites are obligated.
In the Responsa, Binyan Tzion 8, we learn that according to the Gaon Natan Adler, women are obligated to hear Parshat Zachor, in fact he insisted that his maidservant hear it as well. It is not a positive precept dependent on a set time for there is no insistence on a specified time, only that it be read once a year, therefore women are obligated.
Rosh, Brachot 7:20 states that the public reading of Parshat Zachor is DeOraita (a mitzvah from the Torah). Therefore women should hear Parshat Zachor in synagogue.
According to Magen Avraham, remembering the blotting out of Amalek is fulfilled by hearing about the incident with Amalek, “And Amalek came” (Shmot 17:8) which is the Torah reading on Purim morning. Mishna Brura disagrees since the incident in Shmot does not mention the blotting out of Amalek and therefore requires the reading from Dvarim.
We see from here that according to many opinions, women are obligated in hearing Parshat Zachor. Many synagogues read Zachor again at the end of the service as well, just in case not everyone was there during Torah reading including parents of young children.