According to rabbinic sources, women, children, and slaves, are not required to fulfill any commandment which is classified as a "מצות עשה שהזמן גרמא" (mitzvat asei shehazman gerama), a positive commandment dependent on time:
וכל מצות עשה שהזמן גרמה אנשים חיבין ונשים פטורות, וכל מצות עשה שלא הזמן גרמה אחד אנשים ואחד נשים חיבין. (Mishna Kiddushin 1:7, Hebrew Wikisource)
And every positive commandment which is time-dependent, men are obligated and women are exempt. And every positive commandment which is not time-dependent, both men and women are obligated. (Mishna Kiddushin 1:7, English Translation, English Wikisource)
Tzitzit is considered a positive commandment dependent on time, since there is no obligation to wear tzitzit at night:
ר' שמעון פוטר את הנשים מן הציצית מפני שהיא מצות עשה שהזמן גרמא (Tosefta Kiddushin 1:10)
R. Shimon exempts women from tzitzit since it is a positive commandment dependent on time. (Tosefta Kiddushin 1:10, my translation)
ר' שמעון פוטר את הנשים ממצות ציצית שהיא מצות עשה שהזמן גרמא שהרי כסות לילה פטור מן הציצית (Yerushalmi Berakhot 3:3)
R. Shimon exempts women from the obligation of tzitzit which is a positive commandment dependent on time since night clothes are exempt from tzitzit. (Yerushalmi Berakhot 3:3, my translation)
ת"ר: איזוהי מצות עשה שהזמן גרמא? סוכה, ולולב, שופר, וציצית... (Bavli Kiddushin 33b, Vilna Edition, Hebrew Wikisource)
Our Rabbis taught: Which are affirmative precepts limited to time? Sukkah, Lulab, Shofar, fringes... (Bavli Kiddushin 34a, Soncino Translation)
Therefore, women are not obligated to wear tzitzit.
