Leonardo, the first child of Cruz, 38, and 43-year-old husband Javier Bardem, another Spanish big-screen star, was born in January 2011 at the Cedars Sinai Hospital in Los Angeles.
The pair of Oscar-winning performers married in July 2010 in The Bahamas.
Cruz, who was nominated for a Goya – Spain’s equivalent of the Oscar – for her performance in “Volver a nacer”, will not be able to attend Sunday’s gala in Madrid due to a scheduling conflict, said publicist Javier Giner.
The actress is in the US as a result of her work, he said.
Monica Cruz, the actress’s younger sister, announced her own pregnancy by artificial insemination earlier this year.