"Those behind the calls for lynching must be made to feel the full force of the law," said Bernhard Witthaut, chairman of the GdP police union, the Die Welt newspaper reported on Friday.
It cannot be tolerated, he added, that "some users of social networks think they can revive Wild West methods in our democratic society."
A 17-year-old was arrested last week in the coastal town of Emden, and police let it be known he was their chief suspect.
But he was released on Friday after evidence ruled out any involvement in the murder of 11-year-old Lena whose body was found in a car park in the town centre on the evening of March 24th. She was buried in a private ceremony on Friday.
The suspect's arrest on Tuesday prompted an outcry in the town, and a crowd of angry citizens gathered in front of the police station.
News of the arrest also quickly spread on social networks, where users unleashed an outpouring of hate and calls for violence against the young man, whose name and address are reportedly common knowledge among local residents.
Now police have opened a case against an 18-year-old Facebook user believed to be responsible for the worst of the online threats, public prosecutor Bernard Südbeck told radio station NDR on Friday.
Berlin criminal lawyer Martin Heger said public messages on Facebook should be considered "public provocations."
“Public incitement to crime" is punishable under German law with fines and jail sentences, reported Die Welt.
Meanwhile, authorities are facing growing criticism over their handling of the case. Critics say they were too hasty in releasing a public appeal.
"Police and prosecutors have an interest in a rapid outcome to their investigation," conservative politician Hans-Peter Uhl told the regional Kölner Stadt-Anzeiger newspaper on Saturday.
"That's why they're sometimes rather hasty and too often risk a public appeal too soon. We're seeing this happen more and more often," said Uhl, who is domestic affairs spokesman for the conservative Christian Social Union parliamentary faction.