"We have taken over the case," said a spokesperson of the federal prosecution service, which deals with crimes motivated by political and religious extremism
Police and prosecutors issued a joint statement on Sunday to say that they had taken a 45-year-old man into custody Saturday over the shooting death in early June of prominent local politician Walter Lübcke, a member of Chancellor Angela Merkel's CDU party.
"The arrest came on the basis of DNA evidence and the suspect appeared this afternoon before an investigating judge in Kassel," the western city where Lübcke was killed, the authorities said.
READ ALSO: Mourners gather in Hesse for funeral of murdered CDU politician
They declined to comment on a possible motive, saying they would offer further information to the media about the arrest and the investigation's progress in the coming days.
However the Frankfurter Allgemeine Zeitung daily reported that the suspect "comes from the far-right scene", without providing further details.
The Bild newspaper, citing unnamed investigators, said the suspect "could belong to the right-wing extremist scene".
Lübcke was shot in the head at close range on the terrace of his home in Kassel, around 160 kilometres (100 miles) northeast of Frankfurt.
READ ALSO: Politician in Hesse killed with shot to the head
Investigators say it is unclear why the 65-year-old was killed, but a possible political motive has not been ruled out, given he had previously received numerous death threats.
Lübcke, the head of the city administration in Kassel, had spoken out in defence of migrants at the height of Europe's refugee crisis in 2015, drawing the fury of the far right.
Since his death, hundreds of posts from social media accounts tied to right-wing extremists hailed his murder.
As The Local reported, hundreds of mourners gathered for Lübcke's funeral which took place on Thursday in Kassel.
At his service held in the Martinskirche in Kassel, state government head Volker Bouffier, also of the CDU party, said: "It is a sad, painful and almost incomprehensible occasion that brings us together.”