Ms Ardern has been a list MP since 2008, standing in Auckland Central against National minister Nikki Kaye.
She has never stood for the Labour leadership in the three contests since 2011 but she was on Grant Robertson's ticket following the general election last year and he had anointed her as his deputy.
Until now, Ms Ardern has been around 0.5 to 1.5 as preferred Prime Minister. But today she has jumped from 0.5 in April to 3.9 per cent (up 3.4 points). She is well behind Mr Little, who is steady on 11.6 per cent.
Both she Mr Little rate miles behind Prime Minister John Key as preferred Prime Minister - he is preferred by 63.7 per cent, down 0.9 from April. Preferred Prime Minister questions are unprompted - no names are suggested.
But the poll also asked respondents to select their preferred leader to succeed Mr Little from four current front benchers: Ms King, who scored 21.8 per cent; Mr Robertson, who scored 18 per cent; Ms Ardern on 20.1 per cent, and housing spokesman Phil Twyford, with 4 per cent.
Preferred Prime Minister
John Key 63.7 (down 0.9)
Andrew Little 13.3 (down 0.6)
Winston Peters 11.6 (down 0.4)
Jacinda Ardern 3.9 (up 3.4)
Helen Clark 2.6 (up 1.6)
Metiria Turei 0.9 (up 0.6)
James Shaw 0.6 (up 0.6)
Q: If Andrew Little were to step down as Labour leader during this term, who do you think would his best replacements as Opposition leader?
Annette King 21.8
Jacinda Ardern 20.1
Grant Robertson 18.0
Phil Twyford 4.0
None of the above 10.5
Don't know/ refused 25.7
The poll of 750 eligible voters was conducted between August 14 - 24.