Fatima gave birth to Jude Telesia Savea by caesarean section at Wellington Hospital on Thursday morning.
"Welcome to the world Jude Telesia Savea, 7.65pounds of pure joy and happiness. Mummy and daddy love you so very much," Fatima posted on Instagram after the birth.
Jude is Hurricanes wing Savea's second daughter, but the first with Fatima.
Fatima had previously spoken about the couple's difficulties in getting pregnant and how they'd even considered adopting a child, before finding out they were pregnant earlier in the year.