Maradona's daughter Giannina gave birth in Madrid to son Benjamin, whose father is Argentina striker Sergio Aguero.
The Atletico Madrid player has often been likened to World Cup winner Maradona, who now manages the national team.
Maradona was in the Spanish capital for the birth of his first grandson, while Aguero, 20, missed Atletico's training session earlier in the day.
Atletico offered their congratulations in a statement on their official website.
"During the afternoon of Thursday 19 February Benjamin was born in a Madrid hospital. The delivery went without problems and the mother and baby are in perfect condition," it said.
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