They have also been served on former Prime Minister Bill English, and Ministers Paula Bennett, Steven Joyce and Anne Tolley, English's former chief of staff Wayne Eagleson and campaign press secretary Clark Hennessy.
Brendan Boyle, the head of the Ministry of Social Development, has also been targeted.
Asked whether it was appropriate for the Deputy Prime Minister to be serving papers on a chief executive and journalists, Ardern said her conversation with Peters on the matter was brief.
"It didn't include all details of who would be involved. But I actually have no comment to make on it. It is an issue for Mr Peters and it is a personal matter."
Peters, aged 72, revealed during the campaign after media inquiries that he had been overpaid superannuation for seven years, which he immediately repaid.
Boyle told Tolley about the matter under the "no surprises" policy by MSD, and she had told Eagleson. Boyle had consulted State Services Commissioner Peter Hughes, who in turn consulted Solicitor General Una Jagose, before Tolley and Bennett were told.
During the campaign Peters said there was a "disgusting little cartel playing filthy politics", and he singled out Boyle, saying he was politically motivated and had "form".
Peters said that was a reference to him having released official documents during the 2008 campaign on the matter of Bill Liu's controversial citizenship approval by former Associate Immigration Minister Shane Jones, now a NZ First MP and new Forestry, Infrastructure and Regional Economic Development Minister.
High Court proceedings for a hearing on Peters' legal action, a precursor to a damages claim, have been set down for December 13.
Bennett confirmed she had now been served through a representative.
"Looks like a worthless fishing expedition. Would have thought [Peters] had actual work to do."
Murphy also labelled the legal action a "fishing expedition", and noted the papers had been signed on September 22 - the day before the election.
"Peters is seeking journalist phone records, notes, emails in regard to the stories disclosing his super windfall," Murphy tweeted.
"And copious documentation, phone records from Paula Bennett, Joyce, Eagleson, Tolley, English and Brendan Boyle.
"It is a real fishing expedition. Even the lawyers recognise [that] of the defendants 'some will have tortious liability, some will not'."
Hennessy wrote to the Herald saying: "I strongly deny any involvement in this matter or anything to do with Mr Peters' personal life."
Peters is currently in Vietnam ahead of Asia-Pacific Economic Co-operation (Apec) meetings.