The Rashba (Rav Shlomo Ben Aderet of Barcelona, 1235-1310), in one of his more famous responsa, addresses the case that arose in a community in which the only Mohel asked to be paid for performing Beritot, but there was a father who could not or did not want to pay the Mohel to circumcise his son. In such a case, the Rashba rules, the Bet Din must force the Mohel to perform the Berit for free. The Rashba sternly condemns the Mohel for demanding payment for performing this Misva, writing that it is inappropriate to insist on receiving payment for performing a circumcision.
Indeed, the Mishna in Masechet Bechorot establishes that one should not receive payment for performing Misvot such as serving on a Bet Din, or giving testimony before a Bet Din. Seemingly, then, as the Rashba writes, it would be improper for a Mohel to ask for compensation for performing a Berit.
Of course, nowadays it is common for Mohalim to charge a fee for this service, and the question arises as to whether this practice is acceptable, and, if so, on what basis this is allowed.
Hacham Bension Abba Shaul (Israel, 1924-1998) writes that although ideally, a Mohel should perform the Berit for free, without asking for payment, nevertheless, he may request compensation for this service, for several reasons. Firstly, when parents of a newborn child ask a Mohel to perform the Berit, they generally ask him to perform the Berit on their terms – meaning, to show up at a certain place at a certain time. If the parents bring the child to the Mohel to be circumcised at a time that is convenient for the Mohel, then perhaps there is room to question the propriety of demanding payment. But once the parents ask the Mohel to accommodate their preferences, and to be at a certain place at a certain time, they are taking the Mohel away from other things he might have wanted to do at that time, and he is therefore entitled to payment.
Additionally, Hacham Bension writes, the Mohel generally visits the baby before the Berit to determine that he is fit for circumcision, and then again after the Berit to follow up and ensure the wound is healing properly. These visits are not part of the Misva of Mila, and thus the Mohel is justified in asking for payment for these visits. Moreover, the Mohel incurs expenses for his equipment, for which he is entitled to be compensated.
For these reasons, it is acceptable for a Mohel to accept payment, although Hacham Bension emphasizes that ideally, a Mohel should perform the Misva free of charge. (This was also the position of Rav Yosef Shalom Elyashiv.)
It should be noted that this applies even in the case of a Berit performed on Shabbat. Although it is forbidden to receive payment for services provided on Shabbat, the Shulhan Aruch rules that a congregation is allowed to pay a Hazan and a Rabbi for their work on Shabbat, as their work involves a Misva, and this would certainly apply to performing a Berit Mila, as well. Additionally, as mentioned, the Mohel visits the baby before and after the Berit, and thus he may receive payment for performing the actual Berit as part of his overall payment, which includes his visit before and after the Berit (based on the Halachic concept known as "Habla’a").
Interestingly, a number of Poskim raised the possibility that a Mohel who is receiving payment for a Berit might have a different Halachic status than a Mohel performing a Berit for free. One example arises when Tisha B’Ab falls on Shabbat and is thus delayed until Sunday, and a Berit is being performed on that Sunday. In such a case, Halacha absolves the father and the Mohel from fasting that day. Since that day is not the actual date of Tisha B’Ab, the fasting obligation is less stringent, and thus the Mohel is exempt due to the special joy of a Berit Mila. However, the Nehar Misrayim (Rav Raphael Aharon Ben Shimon, 1848-1928) raised the possibility that this would not apply in the case of a Mohel who receives payment for performing the Berit. In such a case, the Mohel performs the Berit simply as a job, and thus perhaps he is not included in the special joy of the Misva such that he should be absolved from the fast. Likewise, the work Hitorerut Teshuba (Rav Shimon Sofer of Erlau, 1850-1944) raised the possibility that if a Mohel who is receiving payment for a Berit is present in the synagogue, Tahanunim are not omitted. Although generally the presence of a Mohel who will be performing a Berit that day exempts the congregation from reciting Tahanunim, the Hitorerut Teshuba questions whether this applies even in the case of a Mohel who is being paid for the service.
Summary: While it is admirable and praiseworthy for a Mohel to perform a Berit Mila for free, it is perfectly legitimate for him to request compensation, even for a Berit performed on Shabbat.