Ms Kandiah was found dead in her apartment with multiple stab wounds.
A foreign media report yesterday said the accused man had worked as a waiter in a Basel restaurant.
It said he disappeared shortly after the killing and that Basel police had claimed repeated clashes took place between him and the victim, who they said was his partner.
The arrested man was granted interim name suppression when he appeared in the Auckland District Court yesterday.
His extradition case was adjourned until next week.
He stood in the dock with his arms folded across his chest, and Judge Emma Aiken said he appeared "rather stunned" to be there.
Prosecutor Katie Hogan was acting on instruction from Crown Law on behalf of Switzerland to have the man extradited.
His lawyer requested the case be adjourned to allow time to build a case against extradition.
Neighbours at his business address said he had owned the business for a short period.
A local resident said a woman was often at the business "and she was always really nice".
Another neighbour said they were "great neighbours, it's great having them next door".
New Zealand and Switzerland do not have an extradition agreement, but police, through Interpol, had been working with Swiss authorities since confirming the man's identity and living arrangements in Auckland in late 2011.
He lived in Switzerland from 1990 until late 2000, police said.
When he was arrested yesterday, he was also given a letter from the Department of Internal Affairs, telling him that his citizenship, granted in 2004, could be revoked, police said.
Immigration New Zealand said the man was granted residence in 2002.
A spokesman from the Swiss Federal Justice and Police department said a formal request for extradition had been submitted on June 30 to New Zealand authorities.
How the case unfolded
Dec 2000: 23-year-old Kavitha Kandiah is found dead with multiple stab wounds in her apartment in Basel, Switzerland.
2001: A man who police say is the dead woman's former partner arrives in New Zealand under a false identify and travel documents.
2004: He is granted New Zealand citizenship.
2011: New Zealand police, working with Interpol, confirm the man's identity and living arrangements in Auckland.
Yesterday: A 42-year-old small business owner is arrested in Auckland. He appears in Auckland District Court in connection with Ms Kandiah's killing.
