Her third child, Aseefa, was also a just a few months old when she assumed office for the second time in October 1993.
The Queen had two of her four children during her reign - Prince Andrew and Prince Edward.
Andrew was born in 1960, almost eight years after she ascended the throne in 1952.
Her eldest, Prince Charles, would have been almost four at the time, and her second-born, Princess Anne, would have been almost two.
Further back in history, Queen Victoria had nine children during her reign from June 20, 1837. Her first child, also Victoria, was born in 1840 and her youngest, Beatrice, was born 17 years later in 1857.
However, while Ardern may not be the first to have children while running a country, she could be the only one of today's female leaders to have one.
When it comes to female heads of state today, British Prime Minister Theresa May was unable to have children, as she told the Telegraph, "it just didn't happen".
Prime Minister of Iceland, Katrin Jakobsdottir, 41, just a few years older than Ardern has three sons.
She assumed office in November last year, when her youngest would have been about 6, and her eldest 12.
Meanwhile another leader close to Ardern's age, Ana Brnabic, Prime Minister of Serbia, has no children.
While other leaders a few years older have children, none were likely to have been born during their time in office.
Estonia's President Kersti Kaljulaid, 46, assumed office in late 2016 when her youngest at the time was just 7.
President of Peru Mercedes Rosalba Aráoz Fernández, 56, has an older daughter and the President of Singapore, Halimah Yacob, 54, has five children - none of whom are likely to be in infancy.
President of the Marshall Islands Hilda Heine assumed office in January 2016, when she was in her early 60s, with four children none of whom were likely to have been babies at the time.
Tsai Ing-wen, 61, president of the Republic of China (commonly known as Taiwan) is unmarried and has no children.
None of the handful of other heads of state appears to have young children.