Marinova, who was a board member of the Ruse-based TV station TVN - one of the most popular TV channels in north-eastern Bulgaria - had reported on an investigation into alleged corruption involving European Union funds.
The minister said investigators had spoken to Marinova's family and friends and "there is no apparent link to her work".
Bulgarian national radio, citing what it said was unconfirmed information from Interior Ministry sources it did not name, earlier reported that "a Romanian citizen with a passport from Moldova" had been detained.
Bulgarian authorities said they were investigating both professional and personal motifs for her murder.
On Monday, hundreds of mourners in Bulgaria held vigils for Ms Marinova.More news: PHCC partners with WEYAK to create mental health awareness among youth
Ms Marinova is the third European journalist to be killed in the past year.
He quoted Mr Juncker as saying previously that "too many" journalists are being intimidated, attacked or murdered and that "there is no democracy without a free press".
Some observers believe the murder could be linked to Marinova's work.
An episode of her programme aired on September 30 featured interviews with two investigative journalists from Bulgaria and Romania who had been working on corruption allegations.
The brutal killing of 30-year-old Viktoria Marinova - who presented a current affairs talk programme called "Detector" for the small TVN television channel - has shocked the country and drawn worldwide condemnation.More news: After 1st postseason cycle, Brock Holt returns to Boston’s bench
Journalists' groups and foreign officials expressed shock.
Ms Marinova had presented a recently relaunched current affairs programme called Detector for the TVN television channel in Ruse. Caruana Galizia was killed in a vehicle bombing in October in Malta and Jan Kuciak was murdered in Slovakia in February.
"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.
While the reporter did not appear to have been intimately involved in uncovering the alleged fraud, her show touched on a sensitive subject in Bulgaria, where corruption is endemic.More news: Drew Brees passes Peyton Manning's record as Saints beat Redskins
And even some of Marinova's fellow journalists were not convinced that she was killed because of her reporting.