Thanks to God everything went perfectly.
The Argentinian confirmed Ciro's arrival in an Instagram post on Saturday afternoon, writing in Spanish: "Welcome Ciro!"
The club tweeted: "Change to the squad".
Messi missed a league game for the first time this season so he could attend the birth of his third son Ciro.
Colombia defender Yerry Mina, a January signing from Palmeiras, replaces Messi, who will return for the midweek game against Chelsea. He has started 26 of Barca's 27 games, while he came off the bench against Espanyol on February 4.
Barca are still unbeaten in the league and lead the standings with 72 points, 11 clear of Atletico Madrid who host Celta Vigo on Sunday.
The Argentine and his wife Antonella Roccuzzo announced last October they were expecting a third child.
Barcelona now sit top of La Liga, eight points clear of closest challengers Atletico Madrid.