The Nashville actress, 25, and her Ukrainian boxer fiancé Wladimir Klitschko, 38, have named her Kaya Klitschko.
In a statement, the couple said: "We are over the moon and madly in love!"
Kaya was born last Tuesday and weighed 7lbs, 14oz and measured 20 inches.According to the Parentdish baby names generator, the name Kaya is of Japanese origin and means 'adds a place of resting'.
Hayden and Wladimir announced their engagement in October 2013 after they began dating four years earlier.
The pair were together for two years before breaking up in May 2011.
They resumed their relationship early in 2013 after Hayden had a brief romance with NFL player Scotty McKnight.
Hollywood star Hayden shot to fame in 2006 as cheerleader Claire Bennet in cult show Heroes.
Her most recent role was as Juliette Barnes in musical drama Nashville, for which she was nominated for a Golden Globe last week.
In November, Hayden told Hello magazine she was excited about having a daughter.
She said: "I'm thrilled that I am having a girl first because I feel like I know a lot about raising a strong woman."
Hayden also discussed how she expected to gain a little weight when she got pregnant, but did not realise how much she would actually put on.