The woman called police, but the man could not be found despite searches by officers and a police dog unit.
"This was a very frightening experience for the victim, in the place where everyone should expect to feel safe," Detective Derek Elima of Waitakere police said.
"We're obviously very keen to catch this man as soon as possible. This man may have been drinking somewhere in the area prior to this attack."
The man was described as being of medium to solid build and wearing a hoodie.
"It was the Sunday night of Father's Day that this happened, and if you were in the Glen Eden area, we'd ask that you think back and recall if you saw someone fitting this description."
Anyone with information could contact Mr Elima on 09 839 0600 or Crimestoppers, anonymously, on 0800 555 111.