Messi and his girlfriend Antonella Rocuzzo have named the boy Thiago.
Barcelona had excused the 25-year-old Argentina forward from training to attend his son's birth at a hospital in the Spanish city, Sport24 reports.
According to the report, in a recent interview, Messi had said he was looking forward to becoming a father.
"I'm prepared for Thiago 's arrival, it is very exciting. It makes you think of things in a different way. You can no longer just think about yourself, you think about him, and how you hope he doesn't have any problems," Messi said.
Meanwhile, Barcelona coach Tito Vilanova  said he still expected Messi to play in the Spanish league match against Celta Vigo at Camp Nou stadium.
"Leo didn't attend training, but tomorrow he will play in the match. If everything goes well, he will come to play. It doesn't change our plans at all that he didn't train today," said Vilanova. (ANI )