Messi was replaced by Yerry Mina for the game at La Rosaleda, with Barcelona citing "personal reasons" for his absence.
Messi confirmed the arrival of Ciro on Instagram, publishing a photograph of the newborn holding his father's hand and revealing that everything had gone well. "We are very happy". This is the first time this season that the 30-year old has not been included in the matchday squad for a league game.
Messi and his wife, Antonella Roccuzzo, have two other sons - Thiago, born in 2012, and Mateo, born in 2015.
Last weekend, Messi netted the only goal of the game as Barcelona recorded a 1-0 victory over title rivals Atletico Madrid at Camp Nou.
Barcelona now sit top of La Liga, eight points clear of closest challengers Atletico Madrid.