The FC Barcelona player had appeared to announce the arrival of the couple's son via his Twitter and Facebook pages in the early hours of Friday morning (December 28).
"Ya ha nacido nuestro hijo! Estamos muy felices! Gracias a todos por vuestros mensajes," he originally wrote on Twitter.
The message, translated in English, states: "Our son has been born! We are very happy! Thank you all for your messages!"
However, when pressed as to what the baby's name was, Pique updated his Facebook and Twitter accounts again to say: "Ya tiene nombre! Se llama Inocencio! Feliz Día de los Inocentes a todos!" ("The baby already has a name! He is called Inocencio! Happy Day of the Holy Innocents to you all!")
'Day of the Holy Innocents' (Día de los Santos Inocentes) takes place on December 28, and has become synonymous with practical jokes and pranks in Spain and other Spanish-speaking nations in a manner similar to April Fools' Day.
The couple, who began dating two years ago, announced the news that The Voice coach Shakira was pregnant in September.
Shakira and Piqué recently unveiled a sonogram of their son.
Watch Shakira with Pitbull in a video clip for 'Get it Started' below: