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The party's overall support fell from 30.5 per cent last month to 26.5 per cent this month.
Broken down into gender support, women's support for Labour fell from 33.4 per cent last month to 29.1 per cent; and men's support fell from 27.6 per cent last month to 23.9 per cent.
Labour has fairly consistently had greater support among women than men since Helen Clark became Prime Minister but male support has never been so low in Herald DigiPoll records going back to 1999.
Conversely National is disproportionately supported by men, with 58.5 per cent of men supporting the party compared with 51.2 per cent of women.
Its overall poll rating went up from 50.4 per cent last month to 54.9 per cent.
There are even more stark gender splits in support for the Greens and for New Zealand First in the poll, with women going for Green and men for New Zealand First.
The Greens are supported by 13.1 per cent of women compared with 6.6 per cent of men; New Zealand First are supported by 6.3 per cent of men and 3.1 per cent of women.
Mr Cunliffe said it was hard to tell whether his speech to a domestic violence symposium was behind the fall.
"It may have had some effect. I certainly don't resile from the comment that family violence and domestic violence is something all New Zealanders need to consider carefully and to take some responsibility for.
"At no time have I suggested that all men are guilty of it."
Mr Cunliffe's speech was praised by many of the women at the family violence conference. In his speech, he said: "I'm sorry for being a man, because family and sexual violence is overwhelmingly perpetrated by men."
But it has also been criticised and cited by Labour life member and former MP Dover Samuels as one of the reasons he is not voting Labour this election.
Mr Cunliffe said he had clarified what he meant and was not planning to give another speech on it.
In terms of geographic support, National has disproportionately more support in Auckland compared with the rest of the country - 57.7 per cent to 53.5 per cent.
But there is no greater or lesser support for Labour in Auckland, with 26.6 per cent of Aucklanders backing it compared to 26.3 per cent for the rest of the country.