The Y Tu Mama Tambien star and his partner Camila Sodi welcomed little Fiona, weighing six pounds (2.7 kilograms), in Mexico City, Mexico.
Luna has revealed the couple named the new baby after his late mother, who was killed in a car crash when he was just two years old.
A statement from the pair, released to People.com, reads, "We're very grateful to everyone who has been thinking of us and who has respected the intimate moment we're experiencing now - the arrival of the family's newest member."
The couple is also parents to 22-month-old son Jeronimo.
The Y Tu Mama Tambien star's wife Camila Sodi is expecting their second child, who will be a little brother or sister to the couple's 17-month-old son Jeronimo.
A statement from the star given to Latina.com reads, "We want to confirm that Camila and I are expecting our second child. We've celebrated the news and it has brought great joy to our lives."
Luna married Sodi in February of 2008.