Peters, 75, will have a post-operative period of recuperation at home, a statement said.
"I remain confident of a quick return to work - as well as being fighting fit for the election campaign, which is typically physically gruelling," Peters said in a statement.
The unexpected leave means New Zealand First will combine its campaign launch with the party AGM on July 19.
The party's bid for electoral seats in Northland is launching this Sunday, spearheaded by Northland and Whangarei candidates Shane Jones and David Wilson.
In recent polls, New Zealand First has been well below the 5 per cent threshold needed to return to Parliament without a candidate winning an electorate seat.
The latest 1 News Colmar Brunton poll had the party on 2 per cent, but Peters dismissed this at the time as "rubbish".
"Stand back and watch, and see what's going to happen," Peters said in response to the poll at the end of June.
New Zealand First usually does better on election day than in the polls.
Peters was on 2 per cent support in the preferred Prime Minister stakes in that same poll.
Last year Peters took a four-week break after a serious operation.
"I went into hospital for a serious operation," he said at the time. "I got an infection, that's what set me back so far."
Asked about the operation later, Peters told reporters it was a private matter.
"It's none of your business. How about I ask you about your life?" he told media.
Retiring National MP Paula Bennett, then National's deputy leader, sent Peters some flowers when he was in hospital last year.
It was a tongue-in-cheek gesture following reports that Peters' legal team had discussed Bennett's resignation as a condition for settling legal action between them.
Peters described the gesture as being in "seriously bad taste" and complained the flowers Bennett photographed herself with were significantly nicer than the ones he was actually sent.