Baby Alice, weighing 3 kilograms at birth as reported by Nine, was born prematurely.
"This tiny human busted out and joined us a tad earlier than expected & I can’t wait to introduce you to her," Kate, 36, wrote on Instagram.
The high-profile yoga instructor continued, "In the meantime we’re taking some time to snuggle her close & slowly introduce to her to this big beautiful world".
Andrew, 44, and Kate have been together for almost two years. This is their first child together.
The former Newcastle Knights has two sons from two previous marriages.