Norway's Sydvest (South West) Police district confirmed the arrest at a press meeting on Tuesday morning.
The accused is reported to have denied killing the girl but has admitted being at the place where she died. He turned himself in to police, news agency NTB reports.
The 17-year-old was previously known to police but not in relation to any form of violent crime, the police confirmed.
In a case that has shocked Norway, 13-year-old Sunniva Ødegård is reported to have been talking to a friend on her telephone while walking home, before saying “shit” as the call was suddenly cut off.
Police said at the press meeting on Tuesday that their inquiries had led them to the 17-year-old, who was interviewed on Monday.
He may be remanded in custody on Tuesday.
“The suspect and Sunniva are both from Varhaug and in the same age group, but we do not know how well they knew each other. He is known to the police, but not due to violence,” police lawyer Herdis Traa said according to NTB's report.
The suspect is a Norwegian citizen.
Section leader Bjørn Kåre Dahl said that the investigation was still at a very early stage and that police had not yet determined the cause of death.
“An autopsy of Sunniva will be carried out today [Tuesday, ed.] so we do not yet have a certain cause of death,” Dahl said.
Police are still looking for potential witnesses and are carrying out forensic examination of the path where 13-year-old Ødegård was found.