But they said it does not appear, at least at this stage, that the murder was linked to her work as a journalist.
The suspect was picked up late on Tuesday at the request of Bulgarian authorities, Interior Minister Mladen Marinov told a news conference.
“We have enough proof linking this person to the scene of the crime,” he said.
German police confirmed a 20-year-old man was arrested in the town of Stade near Hamburg on suspicion of raping, robbing and killing Marinova.
A German police statement said that the process of extraditing the man to Bulgaria had begun and that a request had been filed with the relevant regional court.
Such procedures under the European arrest warrant can take anything from a few days up to several weeks to complete.
Bulgaria's chief prosecutor, Sotir Tsatsarov said “at this stage, we do not believe that the murder is linked” to Marinova's work. “But we are continuing to look at all hypotheses.”
“The evidence that we have at this stage leads us to believe it was a spontaneous attack to sexually abuse the victim.”
The body of 30-year-old Marinova, who worked as an investigative reporter and TV presenter for broadcaster TVN, was found on Saturday in parkland near the river Danube in the northern city of Ruse, Bulgarian media reported.
Preliminary investigations showed the cause of death was blows to the head and suffocation.
The murder was described as “exceptionally brutal,” said Marinov. Bulgarian police confirmed she had been raped before she was killed. Marinov said the country's top murder investigators had been sent to Ruse to work on the case.
The attack has shocked the country and drawn international condemnation amid speculation the murder could be linked to Marinova's work as a journalist. The first episode of Marinova's new show Detektor, which aired on September 30th, featured interviews with two investigative journalists working on a corruption investigation into misuse of EU funds.
She is the third journalist to be murdered in Europe in the past 12 months after Jan Kuciak in Slovakia in February and Daphne Caruana Galizia in Malta in October 2017.