Genesis:  21:4 – And Abraham circumcised his son Isaac when he was eight days old, as God had commanded him.

Babylonian Talmud – Kedushin 29a: – A woman is not commanded to circumcise her son. This is derived from the verse “as God commanded him”. God commanded him, not her.

Torah Temimah Colloquial Translation on Note #6:

Tosafot ask why a verse is needed to teach this law. Could it not have been deduced from the general concept that women are exempt from all commandments which are time-bound. Since circumcisions may only be performed during the day, we would know that women are not commanded in this mitzvah even without a verse to teach this point.

Tosafot answer this question by stating that there are some opinions that circumcisions that occur after the optimally mandated period of 8 days may be performed either during the day or at night. [Thus, according to those opinions, one would need a verse to explicitly teach that women are not commanded to perform circumcisions.] Most rabbinic opinions, however, are that circumcisions even after 8 days must be performed during the daytime.

This may be the reason that the halachic authorities have omitted explicitly mentioning women’s exemption from this commandment even though the Gemora [cited above] explicitly mentions it. Since we follow the ruling that even circumcisions after 8 days should be performed in the daytime, we can automatically deduce that women are exempt from this commandment. That is why the halachic authorities did not need to record this explicit ruling.

We should also consider the question of why the Gemora taught women’s exemption from our verse rather than from the verse in Genesis 17:13 “You should surely circumcise…”. From that verse is taught the law that a non-Jew should not perform a circumcision because from the word “surely” [in Hebrew it is actually a doubling of the verb] we learn that circumcisions should be performed by one who is circumcised. This same approach is used to teach that women may not be scribes and write tefillin. This is deduced (Menachot 42b) from the verse “you should tie…you should write” – all who are obligated to tie are obligated to write.

Perhaps the answer to this question is based on what Tosafot write in Berachot 20b. There they write that women are obligated to say during the recitation of the blessing after meals the phrase “we than God…for the covenant in our flesh…”. Tosafot state that the reason why women are obligated to say this prayer is because since circumcision is not possible with women, there is no reason to exclude them from the general category of people saying the blessing after meals. This same approach is used (in Gemora Avodah Zara 27a) when discussing whether a woman may perform circumcisions due to the fact that she is in the [legal] category of circumcised people.

We see therefore that it is not possible to exclude women from the obligation to perform circumcisions from the verse “you should surely circumcise…” [since woman would actually fulfill this requirement.]

 Translator’s Note: This Torah Temimah note does not actually address the issue of whether women may perform circumcisions. This note here just addresses the topic of whether women are commanded in the mitzvah or not. The question of whether a woman is permitted to perform circumcisions is addressed by the Torah Temimah in his note on Genesis 17:13, note #36. That comment is located here:  http://temimahblog.com/2017/10/31/parshat-%D7%91%D7%A8%D7%90%D7%A9%D7%99%D7%AA-genesis-1713-may-a-woman-perform-a-circumcision/