She made headlines in November when she breastfed her then 3-month-old daughter in Parliament's debating chamber.
However Ms Prime said she wouldn't be lining up to offer the Prime Minister any advice, but would be happy to offer some tips to Ms Ardern if she asked.
"As a mum myself I know you just get overwhelmed by all the advice people offer, all so well-meaning, but I don't want to overwhelm her."
Those tips include the best way to carry a baby seat - something she learnt from a YouTube video - and advice her midwife gave her when she had her first daughter Hihana who was only six days old when the 2015 Northland byelection was called.
"(The midwife said) As long as whoever has her, as long as they are 100 per cent focused on her, she won't notice the crazy stuff going on around her."
She said Parliament had made huge changes to allow her to be a mum and an MP - including allowing babies in the chamber, and allowing her family to bring Heeni to the door of the chamber.
Ms Prime said other Parliamentary mums had also suggested getting a high chair for the cafeteria and she was hopeful it would be there when they all returned to Parliament.
Ms Prime sent the Prime Minister a message telling her it was " wonderful news" and recounting how her and her mum and sister woke Heeni with their excited screams.
"Congratulations to you both and we are here to support you in any way we can," her message finished.
NZ First leader and Deputy Prime Minister Winston Peters also offered his congratulations.
"On behalf of my NZ First colleagues we wish the Prime Minister and her partner every joy during the next several months as they adapt to a new challenge."
Mr Peters will be the acting Prime Minister during the six weeks leave Ms Ardern takes while Tai Tokerau MP and deputy Labour leader Kelvin Davis will take the party's reins in her absence.
