Mr Hunter said the man invoked his right to silence and shed no light on how he obtained his injury.
Police are still investigating the incident, which happened in Myers Park near Aotea Square.
The 22-year-old with the facial scar will be interviewed again and a decision made as to whether he will face charges.
It is understood he acted in self defence.
A pocket knife found in Aotea Square was believed to be the weapon used in the attack, Mr Hunter said.
The knife has been sent for forensic tests for confirmation it was used in the stabbing.
Anyone with information should call Auckland CIB on 09 302 6400 or Crimestoppers on 0800 555 000.