Spanish media reported the birth earlier on Tuesday, citing a hospital representative, though Madrid’s Clinica Ruber declined to confirm the news and representatives for Cruz and Bardem could not be reached for comment.
Cruz was reportedly still in hospital on Tuesday.
She married fellow Oscar winner Bardem in 2010 and the couple had their first child, a boy named Leo, in Los Angeles two and half years ago.
Cruz and Bardem are the only Spanish actors to have won Academy Awards, both for supporting roles.
They first met on the set of a Spanish film in 1992 but got together after starring in Woody Allen’s 2008 comedy “Vicky Cristina Barcelona.” They are due to appear together in supporting roles in “The Counselor,” a film directed by Ridley Scott, scheduled for release later this year.