Southern tweeted a link to the video of Ardern's comments, made at Wellington airport as she returned to ready for her first day back Parliament after giving birth to her daughter.
Southern wrote: "A blatant display of the limits of "tolerance" and "diversity".
"You say you support multiculturalism / different views / diversity – but you can't even support different opinions being espoused peacefully for one night?
"It's all virtue signalling nonsense."
Southern and Molyneux, Canadian activists whose views often align with those of the far right, have courted controversy wherever they go.
Their official tour response to news that their only speaking event in New Zealand was cancelled was: "Hope you enjoy shariah", a reference to Sharia or Islamic law.
Southern and Molyneux claimed that "powerful forces" prevented them speaking in New Zealand.
The pair's on-again, off-again visit to this country sparked a debate about free speech after Auckland Mayor Phil Goff blocked them from using council venues, saying he did not want such spaces used to stir up ethnic tensions.
They cancelled the trip after the setback but later reconfirmed plans to speak here after the promoter found a new venue.
Immigration Minister Iain Lees-Galloway has said he personally felt their views were repugnant but that there was no grounds to reject their visas.
He dismissed claims that they had been banned from other countries, saying they were prevented from entering for specific purposes.
