"Cash and I are so excited to announce the birth of our daughter, Haven Garner Warren. She was born on Saturday, weighed 7 lbs, and was 19 inches long. Healthy and happy!," Alba wrote.
Alba and Warren, 32, already have another daughter, 3-year-old Honor Marie.
"Big Sister Honor couldn't be more excited about the new addition to our family," the actress wrote on Facebook.
The birth came a week before the opening of the movie "Spy Kids: All the Time in the World," the fourth in the "Spy Kids" series and in which Alba plays Marissa Cortez Wilson, the wife of reporter Wilbur Wilson (Joe McHale), who dedicates himself to hunting down spies.
The production will be shown in "4D," a system that combines the three-dimensional effect with physical effects in the theater synchronized with the action in the film, including smells and movements.