Messi had pulled out of Barcelona's squad for Saturday's La Liga match at Malaga to be present for the birth.
The club tweeted: "Change to the squad. Messi is out for personal reasons and Yerry Mina takes his place."
The Argentinian couple, both 30, first met in their home town, Rosario, in 1996 and started going out a decade later. They were married last year in Rosario.
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Barcelona, who face Chelsea in the second leg of their last-16 Champions League tie at the Camp Nou on Wednesday, have an eight-point lead over Atletico Madrid at the top of La Liga.
(With AFP Inputs)
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