For the highest courts they're formally appointed by the Queen's representative, though the person doing the picking changes depending on the court. In some cases it is indeed a minister, but there are a couple of key differences:
*You can't become a judge at any level if you show any kind of partisanship - which automatically filters the pool of higher court appointments. Chucking political letters at the end of people's names seems weird to someone living in a Westminster system.
*The shortlist is done by the Ministry of Justice, but the civil service is functionally independent of the political parties. There's a good show called Yes, Minister that drives at the relationship between the executive and the legislature and we use the same system. In this case the shortlists are done by the department with input from the Bar Association, the Law Society and sitting senior members of the bench - and the person doing the selections (be it the Prime Minister, the Attorney-General or the Solicitor-General) doesn't have a say in the shortlist or who creates the shortlist.
We also don't have elections for judges. At face value it may sound shady to have a panel of unelected professionals to pick judges but I've long been cynical of having something like that put to the vote.
If you're interested in reading more this would be a solid place to start:
https://teara.govt.nz/en/judicial-system/page-7
