She is also almost equal favourite with veteran MP and deputy leader Annette King to take over the Labour leadership, were anything to happen to current leader Andrew Little.
Today's DigiPoll result follows last week's New Zealand Herald Mood of the Boardroom survey of leading CEOs which rated Ms Ardern as the best performing Labour MP since the election, ahead of Mr Little, Ms King and finance spokesman Grant Robertson.
Ms Ardern has responsibility for small business in the Labour caucus, as well as justice, children, arts, culture and heritage.
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% (up 3.4 points). She is well behind Mr Little, who is steady on 11.6%.
Both she and Mr Little rate miles behind Prime Minister John Key as preferred Prime Minister - he is preferred by 63.7%, 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%; Mr Robertson, who scored 18%; Ms Ardern on 20.1%, and housing spokesman Phil Twyford, with 4%.
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
By Audrey Young of the New Zealand Herald
