The man appeared in the Palmerston North District Court this afternoon and was granted interim name suppression.
He was remanded in custody and is due to reappear in court on Tuesday with the likelihood of facing more serious charges.
Mr Thompson said both the victim and offender are Massey University students, and police have spoken with the victim's parents.
A post-mortem was due to be undertaken at Wellington Hospital tomorrow.
"The post mortem will give us a clearer picture of how the woman has died," Mr Thompson said.
A scene examination was underway and inquiries were being made within the apartment block.
"Over the next few days we will speak with close friends and family of both the victim and offender to try and piece together the events that led to this tragedy," Mr Thompson said.
"We are also working closely with Massey University to ensure those directly affected and the wider student community have access to support services."
Police are not seeking anyone else in relation to this investigation.