During a phone interview with More FM on Monday morning, hosts said they couldn't wait to hear the gender and asked her if she would be doing a Woman's Day story.
"We are not doing any of that stuff for now.
"I'll be hauling her round the country, so it will be hard to hide," she seemed to say.
There is dispute between her saying "hauling her round" and "hauling around".
Ardern had previously told the Herald she and partner, Clarke Gayford, would be keeping the gender of the baby a secret.
Ardern also admitted she and Gayford had a bet as to who would blab the gender secret first.
"I think we've made a mistake in knowing [the sex of the baby], because both of us are taking bets now on who's going to stuff it up," she told More FM.
Gayford said his mum had been knitting the couple a shawl but had been "hiding it whenever someone comes around".
Ardern announced she was pregnant with her first child, due in June, on Friday.
She discovered she was pregnant just six days before she became Prime Minister-elect.