If a firstborn infant’s 31st day – the day when the Pidyon Ha’ben is to take place – falls on Shabbat, the Pidyon Ha’ben is delayed until after Shabbat, and is performed either on Mosa’eh Shabbat or Sunday. It is not performed on Shabbat, since transactions are forbidden on Shabbat, and thus one cannot make a payment to the Kohen for the Pidyon Ha’ben. A number of Halachic authorities (including the Terumat Ha’deshen and Maharshal) addressed the possibility of performing the Pidyon Ha’ben in such a case on Friday, giving the Kohen the money and stipulating that the transaction should take effect only on Shabbat, the 31st day. In practice, however, this is not done, and the Pidyon Ha’ben is instead delayed until Motza’eh Shabbat or Sunday.
This applies as well if the day of the Pidyon Ha’ben falls on Yom Tob. Whether it falls on the first day of Yom Tob or (in the Diaspora) on the second day of Yom Tob, the Pidyon Ha’ben is not performed on that day, and is instead performed after Yom Tob. This applies to all the Yamim Tobim – Rosh Hashanah, Yom Kippur, Sukkot, Shemini Aseret, Pesah and Shabuot.
There is some discussion among the Poskim as to whether a Pidyon Ha’ben may be performed during Hol Ha'mo'ed. The issue revolves around the question as to whether a Pidyon Ha’ben should halachically be considered a "Simha" – a festive celebration, in which case it should not be held during Hol Ha’mo’ed, in light of the principle of "En Me’arbin Simha Be’simha" – we do not combine two Misva celebrations. The Rama (Rav Moshe Isserles of Cracow, 1530-1572) cites two opinions on this matter, and Halacha follows the view that a Pidyon Ha’ben may be performed during Hol Ha’mo’ed. The fact that the words "She’ha’simha Bi’m’ono" are not added to the Zimun service before Birkat Ha’mazon after the Pidyon Ha’ben meal proves that Halacha does not regard a Pidyon Ha’ben as a "Simha," and thus it may be held during Hol Ha’mo’ed. This applies even in the case of a Pidyon Ha’ben "She’lo Bi’zmano" – meaning, if the Pidyon Ha’ben was not performed on the 31st day, and it is already after the 31st day. Even in such a case, the Pidyon Ha’ben may be performed on Hol Ha’mo’ed. (Of course, on Hol Ha’mo’ed Sukkot, the meal must be eaten in a Sukka.)
If the day of the Pidyon Ha’ben falls on a fast day that begins in the morning (Som Gedalya, Asara Be’Tebet, Ta’anit Ester, or Shiba Asar Be’Tammuz), then the Pidyon Ha’ben is performed at night, before the fast begins. If the day falls on Tisha B’Ab, when the fast begins already at sundown the previous evening, the Pidyon Ha’ben should be performed towards the end of Tisha B’Ab, late in the afternoon, and the festive meal is then held at night, after the fast.
If the day of the Pidyon Ha’ben falls during the Sefira period, the Pidyon Ha’ben is performed as usual, and the child’s father is permitted to shave and take a haircut in honor of the event. Music is permitted at the celebration. Likewise, if the day falls during the period of Ben Ha’mesarim (the three weeks from Shiba Asar Ba’Tammuz until Tisha B’Ab), the Pidyon may be performed and celebrated as usual, with music, and meat may be served, even if the event takes place during the Nine Days. However, if the Pidyon Ha’ben is held during the week of Tisha B’Ab ("Shabua She’hal Bo"), only ten people should be invited to take part in the meat meal celebrating the event.
Summary: If the day of a Pidyon Ha’ben falls on Shabbat or Yom Tob, it is delayed until after Shabbat or after Yom Tob. A Pidyon Ha’ben may be held on Hol Ha’mo’ed. If the day falls on a fast day, it is held the night before the fast, and if it falls on Tisha B’Ab, then the Pidyon is performed late in the afternoon of Tisha B’Ab and the meal is held after the fast. During Sefira or the Three Weeks, the Pidyon Ha’ben may be held as usual, even with music, and meat may be eaten at the Pidyon Ha’ben celebration during the Nine Days.