It is the second daughter for Smith, 40, who has a 5-year-old daughter, Fanny, with her cinematographer husband Stephen Lubensky.
Smith, who is best known for her role in Silence of the Lambs, told PEOPLE in October that she and her husband were considering adopting.
"You know, why not?" Smith sad, adding that she and Lubensky have traveled to Africa several times, and filmed a documentary on conservationists in Zimbabwe together. "We still might end up there some time," she said.
The news was first reported by TV Guide.