(Genesis 17:8-9) It was stated: From where do we know that a circumcision performed by a gentile is invalid? Dari bar Pappa in the name of Rav said: from "And you shall keep My covenant" [the duty falls on one who is himself in the covenant]. Rabbi Yohanan said: from (verse 13) "he must surely be circumcised" [Hebrew himmol yimmol, one who is himself circumcised circumcises others]. What is the difference between them? There is a difference regarding a woman. According to the one who derives it from "And you shall keep My covenant," a woman is excluded, since a woman is not subject to circumcision. But according to the one who derives it from "he must surely be circumcised," she is included, since a woman is regarded as one already circumcised. But is there anyone who holds that a woman is not subject to circumcision? Is it not written, "And Zipporah took a flint" [and circumcised her son]? Read it instead as "And she had taken." But it is written, "and she cut off" the foreskin! Read it instead as "and she had it cut off" [by another].
Whether a Gentile May Perform a Valid Circumcision
Yalkut Shimoni on Torah 81:11
(בראשית יז ח-ט) אִתְּמַר, מִנַּיִן לְמִילָה בְּגוֹי שֶׁהִיא פְּסוּלָה, דָּרֵי בַּר פָּפָּא מִשְׁמֵיהּ דְּרַב אָמַר, וְאַתָּה אֶת בְּרִיתִי תִשְׁמֹר רַבִּי יוֹחָנָן אָמַר, (להלן פסוק יג) "הִמּוֹל יִמּוֹל" מַאי בֵּינַיְהוּ, אִיכָּא בֵּינַיְהוּ אִשָּׁה, מַאן דְּאָמַר וְאַתָּה אֶת בְּרִיתִי תִשְׁמֹר לֵיכָּא, דְאִשָׁה לַאו בַּת מִילָה הִיא, וּלְמַאן דְאָמַר הִמּוֹל יִמּוֹל אִיכָּא, דְּאִשָּׁה כִּמְהוּלָה דַּמְיָּא. וּמִי אִיכָּא לְמַאן דְּאָמַר אִשָּׁה לָאו בַּת מִילָה הִיא, וְהָכְתִיב "וַתִּקַּח צִפּוֹרָה צֹר", קְרִי בֵּיה וַתַּקַּח וְהָא כְּתִיב (שם) "וַתִּכְרוֹת" קְרִי בֵּיה וַתַּכְרֵת.