"Mother, father and baby are doing great," their publicists, Ken Sunshine and Nicole King, told The Associated Press.
They said the baby was born at 6:26 p.m. EST Thursday but would not give any other details, including where the infant was born.
It is the first child for Garner and Affleck, both 33, who were married in June.
The confirmation came after several media outlets reported the baby's birth — hours before the time of birth supplied by Sunshine and King.
Us Weekly reported the baby was born sometime before 2 p.m. EST, and E! News said the couple had named her Violet.
Affleck co-starred with Garner in 2003's "Daredevil," her first big movie role, but they didn't begin dating until last year.
Garner was previously married to actor Scott Foley. They were divorced in March 2004 after 3 1/2 years of marriage. Affleck and Jennifer Lopez called off their September 2003 wedding and broke off their engagement in January 2004.
Affleck will star as George Reeves, television's Superman, in the upcoming movie "Truth, Justice, and the American Way."
Garner's ABC series, "Alias," is ending its five-year run in May. Her pregnancy was written into "Alias" for her character, a globe-trotting spy.