Ms Schulze's family in Germany have not reported her missing but her lack of contact with close friends including Katharina Niese prompted the call to police.
"We are looking for our friend Anja Schulze ... Unfortunately, we have no contact since February 2014 and also cannot reach [her]," Ms Niese wrote on the Facebook page of a Swiss news organisation.
"We are very worried for [her] ... I hope we find her and nothing bad happened ... just thinking positive."
Ms Schulze was born in Berlin but was living in Zurich, Switzerland before travelling to New Zealand.
On Facebook Ms Niese said her friend planned to live and work in New Zealand for a year before travelling on to Australia.
Detective Fran Moore of the national police missing persons unit said Ms Schulze arrived in Auckland on December 7. "We know from friends that she told them she travelled around the East Coast, she walked the Tongariro track," she said.
"The next confirmed thing was that she crossed the Cook Strait on the Bluebridge ferry on January 29.
"On the 31st of January she messaged a friend saying she was going to Golden Bay. But where she said she was heading to, it doesn't appear that she actually went - they are not aware of her."
The last time Ms Niese heard from Ms Schulze was on February 2.
Ms Moore said the tourist had been listed as a missing person but a full investigation had not been launched.
"Our best hope of finding her is with help from the public and from other young travellers who might have travelled with her."
Ms Moore said tourists did sometimes change their travel plans and not tell friends and family back home.
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