Alba, 27, best-known for her roles in the TV drama "Dark Angel" and the movie "Fantastic Four," announced last December that she was pregnant and engaged to Warren.
Alba met Warren, 29, on the set of "Fantastic Four" in 2004 where he was a director's assistant. Warren has since moved into producing.
US Weekly said Alba gave birth to her daughter at the Cedars-Sinai Medical Center in Los Angeles over the weekend.
The couple married in a quiet ceremony at the Beverly Hills courthouse on May 19.
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