Milan Pique Mebarak was born at 9.36pm on Tuesday in Barcelona, Spain.
A statement posted on the pop star's site in English, Spanish and Catalan said that "just like his father, baby Milan became a member of FC Barcelona at birth".
The statement also said Milan weighed approximately 6lb 6oz (2.9 kilograms), and that "both mother and child are in excellent health".
Shakira asked fans earlier on Twitter "to accompany me in your prayers on this very important day of my life".
Milan is the couple's first child.