One woman wrote: "God I love you and your complete insistence on being so human. Hooray hoorah to baby poo!"
Another said: "[Love] that you just said 'pooed'! We defo have the best PM in the world!! xo."
While one simply wrote that she was "woman goals".
Ardern and her fiance Clarke Gayford are known for sharing hilarious details of their lives with Neve.
In March, Gayford said on Twitter his daughter had been the victim of a kereru bird's poo.
Ensue hilarity.
"The first child of NZ has been officially coronated," one person wrote.
Another added: "What do they say? That Dad has a great sidestep."
On Friday, Ardern and her ministers began the process of selling their Wellbeing Budget - released Thursday - to New Zealanders after announcing some big increases to social spending and mental health.
Almost $2 billion across five years will be spent on addressing mental health issues.
More than $455 million of that funding has been put towards expanding access to mental health and addiction support, particularly for those with mild to moderate mental health needs.
"We said that we would be a Government that did things differently, and for this Budget we have done just that," Ardern said in the House.
"Today we have laid the foundation for not just one Wellbeing Budget, but a different approach for Government decision-making altogether.
The funding announcement came a day after the Government revealed it would be adopting 38 of the 40 recommendations in the He Ara Oranga report on mental health.