Barcelona footballer Pique wrote: "Our son has been born! We are very happy! Thanks to all for your messages!"
Just a few days before Christmas Addicted To You performer Shakira (35) was spotted shopping for gifts in Barcelona.
The Colombian was recently named as the newest judge on the US version of The Voice, replacing Christina Aguilera.
She had announced her first pregnancy in mid-September.
It also emerged that Strictly Come Dancing star Brendan Cole became a father on Christmas Day.
The 36-year-old dancer's wife of two years Zoe gave birth to a girl, he wrote on Twitter. It is the couple's first child.
The New Zealander wrote: "My wonderful wife & I had the best Christmas present ever. Our baby daughter arrived on Christmas Day. Zoe & Baby doing great! Very precious."