The baby girl was born in July in a hospital in Madrid. The information came to light after Bardem went to register the baby, reported Us magazine quoting Latin Times.
Luna means moon in Spanish, while Encinas is Bardem's paternal surname which means "live oak."
Cruz has been working as a director on a short film in London, starring beautiful model Irina Shayk in the lead role.
The film presents a lingerie collection that Penelope and her sister Monica have created.