The 29-year-old powerhouse was excused training duties in order to watch on a computer in Cardiff as his wife, Alana Raffie, give birth to a baby daughter back in his homeland.
Williams, who is set to face Wales on Saturday, and Raffie have not yet named the baby girl.
All Blacks assistant coach Ian Foster said: "Sonny wasn't training simply because he was monitoring the progress of his wife.
"We're delighted Sonny and his wife Alana had a little baby girl this morning and he was following that event so we're delighted.
"The family's good and it's all on top of Charlie [Faumuina] and Michelle's second child last week, so it's been a week of celebration for the All Blacks with babies."