Baby Satyana is the first child for Hannigan and her husband, actor Alexis Denisof.
The couple met while appearing together on the TV show "Buffy the Vampire Slayer" and married in 2003.
Hannigan is now one of the stars of the sit-com "How I Met Your Mother."
Hannigan's publicist told People magazine she gave birth to her daughter March 24, the actress' 35th birthday.
"They're very excited, and mom and baby are doing great," the representative told People.
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