Ardern said she would be taking six weeks leave following the baby's birth. Deputy Prime Minister Winston Peters would serve as acting prime minister during that time.
"I am not the first woman to multi-task, I'm not the first woman to work and have a baby," she said. "I know these are special circumstances but there will be many women who will have done this well before I have."
The challenges were far more daunting for Bhutto 27 years ago.
"The next day I was back on the job, reading government papers and signing government files," she later wrote.
"Only later did I learn that I was the only head of government in recorded history actually to give birth while in office. It was a defining moment, especially for young women, proving that a woman could work and have a baby in the highest and most challenging leadership positions."
Update: The headline of this piece has been updated to more accurately reflect Bhutto's tenure.