It will be held on December 10, with candidate nominations closing on November 8, less than three weeks away.
Ardern said she had received advice overnight on the potential timing from the Cabinet Office and the Electoral Commission.
"That advice gave me a limited number of possible options given the time of year that we're in - public holidays and so on - and of course needing to take into account the final tally of votes being delivered before we move into significant end-of-year events," she told reporters in Auckland this afternoon.
"I am still disappointed on behalf of taxpayers that we're having this by-election in the first place. It's been triggered by the fact the independent member for Hamilton West has decided to resign in order to run as an independent member for Hamilton West.
"That seems to me to be a complete waste of money."
The major parties have both played down their chances of winning the seat.
Ardern said Labour was going through its usual process ahead of the by-election.
"I don't think anyone thinks the scenario that Hamilton West has just gone through has been particularly edifying. I'm incredibly disappointed about what a Labour candidate has done, so I'm sure that may well be an issue for us, but of course these are the circumstances we find ourselves in.
"We will stand proudly on our record as a government, and what we've been doing in the Hamilton region."
Labour cuts ties with Sharma
Sharma won the seat for Labour in the 2020 red wave with 20,703 votes, well ahead of his National Party rival Tim MacIndoe on 14,436.
But he was expelled from the caucus in August this year for breaching the Labour Party's code of conduct. It meant he was no longer a Labour MP and would remain in Parliament as an independent, but he was still a member of the party.
On the same day, Labour's caucus voted to refer his conduct to the wider party to assess whether his membership should be removed. The leadership then referred the matter to an investigative panel.
On Tuesday, Sharma resigned as an MP, saying he had heard from a credible source that Labour planned to use the waka-jumping legislation to remove him from Parliament in the six months before next year's general election, meaning there would be no need for a by-election.
Ardern, Labour Party President Claire Szabó and top-ranking ministers have all rejected Sharma's claims, saying there was no plan to use the waka-jumping law and that he was speculating. Writ day will be Wednesday, November 2.
Yesterday, Labour confirmed it had recommended that Sharma be expelled from the party membership after an investigation into his conduct.
Szabó published a summary of the events leading up to the decision, saying he had participated actively in the investigation and provided oral and written accounts of his perspective to the investigating panel and full council.
"When we communicated with Gaurav on Saturday 15 October, he said he had recently experienced a bereavement in his wider whānau - which he had also noted on his Facebook page. On that basis, Gaurav requested extra time to document his perspective on our investigation," she said.
"We agreed to his request on compassionate grounds, and gave him an additional opportunity to present any documentation he wished. That window closed yesterday, and we received no further documentation from Gaurav."
The New Zealand Council, Labour's governing body, met yesterday and decided to expel Sharma from the party, with immediate effect.
