According to media reports, the 37-year-old pop star had her baby on schedule by Cesarean section in a Barcelona hospital.
The statement released on Shakira's website read: "We are happy to announce the birth of Sasha Piqué Mebarak, son of Shakira Mebarak and Gerard Piqué, born January 29 at 9:54pm, in Barcelona.
"The name Sasha is of Greek and Russian descent and means 'defender of mankind' and 'warrior.'
"The hospital confirmed that both mother and child are in excellent health."
Shakira and 27-year-old Pique met when he appeared in her music video for the 2010 World Cup song, 'Waka Waka (This Time for Africa)'. They are already parents to 2-year-old son, Milan.
The 'Hips Don't Lie' singer has been very vocal about her desire to continue to expand their family.
"I would love to have eight or nine kids with Gerard - my own futbol team," she said in an April 2014 interview with Latina magazine.