The Barcelona star had earlier pulled out of the squad for tonight’s game at Malaga and was replaced in the travelling party by defender Yerry Mina.
Messi then took to Instagram to announce Ciro had been born, with the message: “Welcome Ciro! Thank God everything went perfect. Mum and he are very well. We are super happy.”
The 30-year-old Argentina international is also a dad to sons Thiago, 5, and Mateo, 2 and has been with his wife Antonella since he was 20.
Earlier this week, Pancho Schroder, Barcelona’s financial and strategy director, admitted he was worried that a “crazy” rival could pay Messi’s £625million release clause.
Argentine ace Messi inked a new deal at Camp Nou last November, with the mega-money buyout clause having been increased following Neymar’s £200million defection to Paris Saint-Germain last summer.
The Ligue 1 side more than doubled the previous world transfer record by prising the Brazilian from Barca, against their wishes.