Catechism of the Catholic Church §1252 — excerpt
The practice of infant Baptism is an immemorial tradition of the Church. There is explicit testimony to this practice from the second century on, and it is quite possible that, from the beginning of the apostolic preaching, when whole "households" received baptism, infants may also have been baptized.
This translation is under copyright, so only the cited words are quoted here. Follow the link for the full text. Translation: English translation of the Catechism of the Catholic Church, 2nd ed. (Libreria Editrice Vaticana), as posted at vatican.va.
Also cites: CDF, instruction, Pastoralis actio: AAS 72 (1980) 1137-1156