The brit milah of a healthy baby is always done on the 8th day, even Shabbat or Yom Kippur, and only during daylight hours! This 8th day is calculated to include the day of birth. If a baby is born, for example, on a Tuesday afternoon, under normally circumstances the Brit would be the following Tuesday, any time during the day. (There is a tradition to do the Brit as early in the day as possible.) A Brit Milah performed prior to this 8th day, or at night, does not comply with Jewish law, and is not considered a valid Brit.
A Brit of a baby delivered by caesarean section, although normally performed on the 8th day, may not be performed on the Sabbath or Jewish holiday. In this case, the Brit is delayed until the next weekday.
Reasons to delay: A Brit Milah is never performed if it poses any danger to the infant. The doctor and/or mohel's advice to delay a Brit for health reasons should always be heeded. In case of jaundice (yellow pigmentation of the skin), the brit cannot be performed; it is delayed until the bilirubin in the blood drops to a safe level. The brit may then be performed without endangering the child. In cases of some illnesses, a delay of seven days following full recovery is required. It is forbidden to postpone the brit for any reason other than health of the child, or in order to obtain a proper Mohel (see above). It is the responsibility of the Mohel, in consultation with the doctor and the family, to determine if a delay is necessary according to Jewish law.
The Brit may be performed in a Synagogue, social hall, or in a private home with complete safety. [Rabbi Moshe Shulman]