Police in Viersen were still holding a 25-year-old man from Turkey in connection with the crime on Tuesday morning.
The man, who is already known to the authorities, fled when police attempted to detain him on Monday. He later handed himself in, but police have not yet confirmed that he is a suspect.
On Monday shortly after midday a 15-year-old girl of Romanian citizenship was stabbed in a park in the town of 75,000 inhabitants. Bild reports that she was called Iulia R. and that she lived with her parents on the outskirts of town.
According to eyewitnesses, she collapsed as blood streamed from the wounds. A homeless man has told local media that he attempted to save her by holding her wounds together.
Emergency services arrived at the scene shortly after and rushed the teenager to hospital, but she died of her injuries shortly after.
Police then started a search in the town for the killer, who witnesses described as being around 1.70 metres tall and "of southern appearance.”
The Rheinische Post reports, based on police sources, that the murderer was romantically involved with his victim.
For reasons of tactical expediency, investigators have provided no further details about the crime, such as whether the murder weapon has been found.
This is the second time within a matter of days that the body of a murdered teenage girl has been discovered in Germany.
Last week, 14-year-old Susanna F.s body was discovered near Wiesbaden in Hesse. Police suspect that she was raped and then murdered. A young Iraqi man has admitted to the murder but denied sexual assault.
Meanwhile, several teenage girls have been the victims of knife crime over the past six months.
In December last year a 15-year-old girl was stabbed to death in a drug store in the southwest of the country. Then in March, two teenage girls, one in Flensburg and one in Berlin, were stabbed to death.
Several of the crimes appear to have been motivated by jealousy on the part of the attacker.
The fact that the suspected murderers have often been asylum seekers has also led to a highly contentious debate on issues such as Angela Merkels refugee policies and the religious and cultural backgrounds of the attackers.
The Alternative for Germany (AfD) charge that Merkel made a momentous mistake by allowing hundreds of thousands of unregistered migrants to enter the country in late 2015. In the wake of the murder of Susanna F. they have called for Merkel and her entire cabinet to resign.
But critics charge the AfD with racism for statements which appear to portray all refugees who fled to Germany as dangers to society.
Their co-parliamentary leader Alice Weidel recently faced harsh criticism for disparaging remarks about girls who wear headscarves.