The man - a Romanian - was being held for 24 hours, Atanasov said.
"We have in custody a person whose alibi we are checking, but for the time being we do not have a concrete suspect".
Bulgarian national radio reported the suspect was "a Romanian citizen with a passport from Moldova".
Late on October 8, the Interior Ministry announced that prosecutors had opened an investigation into the GP Group and froze 14 million euros ($16 million) of its assets, as hundreds of people thronged candlelight vigils in Sofia and Marinova's hometown of Ruse.
Authorities discovered the body of 30-year-old Viktoria Marinova on Saturday in the northern town of Ruse near the Romanian border.
He said Marinova was linked to bivol.bg's investigations because its reporters had appeared on her show.
It remains unclear whether Marinova was killed as a result of her work.
Bulgarian interior minister Mladen Marinov initially denied that Marinova's murder was linked to her reporting, and said there was no evidence she had been threatened.
"I see deliberate attempts to marginalize this killing and manipulate the public opinion that Viktoria was a victim of a random attack or sexual manslaughter", Assen Yordanov said, adding that Marinova was the only TV journalist who had agreed to host his website's journalists to discuss the investigation.
In a July report on the state of media freedom in Bulgaria, Reporters Without Borders said, "Fortunately, no investigative journalists have been killed in Bulgaria for their work, but there are documented murder plans and attempts, cruel, execution-style, beatings, auto arson and bombs targeting investigative reporters".
Bulgaria is regarded as a laggard in the European Union in matters of press freedom, ranking 111th out of a total 180 in this area, according to Reporters Without Borders (RSF).