People.com said the child was born Wednesday.
Poppy is the third child for the "Grey's Anatomy" actress and Christopher Gavigan, co-founder of The Honest Company, which sells eco-friendly products. The couple have been married eight years and are also the parents of Eve Augusta, 20 months, and Luke Hudson, 4 1/2.
"Our hearts are bursting with love and gratitude upon the arrival of our baby girl," the couple told People.com in a statement.
Capshaw is the daughter of actress Kate Capshaw and businessman Robert Capshaw, and the stepdaughter of director Steven Spielberg.
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