Ali Bashar, 20, is believed to have strangled 14-year-old Susanna Maria Feldman after raping her in the German city of Wiesbaden.
He was detained early Friday in northern Iraq following an outcry in Germany after police hunting the fugitive admitted he had fled with his family.
"During interrogation following his arrest, the young man originally from Kurdistan confessed to killing the German girl," said Tariq Ahmad, police chief for the Dohuk area of Iraqi Kurdistan.
"He said that the two of them were friends but that they had a dispute, and that he killed her when the girl threatened to call the police," Ahmad said.
On Friday a senior official in the autonomous Kurdistan region told AFP that authorities were working to transfer Bashar quickly back to Germany to face trial.
That process could prove tricky as there is no official extradition treaty between Iraq and Germany.
The case has put renewed pressure on Chancellor Angela Merkel's government over the decision to open Germany's borders at the height of Europe's refugee crisis in 2015, resulting in the arrival of more than a million asylum seekers.
Bashar arrived in Germany in 2015 along with his parents and five siblings.
He should have been deported after his request for asylum was rejected in December 2016, but he obtained a temporary residence permit pending his appeal.
During this time, he got into trouble with the police on several occasions, including for fights, alleged robbery and possession of an illegal switchblade.
He was also among the suspects for the sexual assault of an 11-year-old girl living in the same refugee shelter.