The Britain's Got Talent judge welcomed Hollie Rose Hughes on January 23.
The news comes after Holden pulled out of auditions in Blackpool, having admitted herself to a London hospital. A spokesperson for Holden and husband Chris Hughes confirmed that the actress had been in a "critical" condition, but is now "stable".
"Hollie Rose Hughes was born on 23 January 2012. She is healthy and weighed in at 6.1lbs but Amanda has been in a critical condition for the past three days," Alison Griffin said.
"She is now stable and we expect her to make a full recovery very soon. We thank you for respecting their privacy at this time."
A spokesperson for Britain's Got Talent added: "We extend our congratulations to Amanda and Chris on the birth of Hollie and wish Amanda a speedy recovery. We look forward to her returning to Britain's Got Talent very soon."
The former Shrek: The Musical star, who suffered a stillbirth last year, said that she had "burst into tears" upon discovering her pregnancy.
> Amanda Holden on pregnancy: "I never dreamt it would happen so quickly"