But they said that, at least for now, the killing does not appear linked to her work as a journalist.
Authorities said she died from blows to the head and suffocation. She told him she was working on a journalistic investigation but did not feel anxious about her safety and had not received threats.
Global bodies charged with the safety of journalists around the world have condemned the murder of Marinova as The Committee to Protect Journalists called on Bulgarian authorities to conduct a "rigorous, thorough investigation" into the killing.
Bulgaria's prosecutor general, Sotir Tsatsarov, confirmed the arrest of Severin Krassimirov, a 21-year-old Bulgarian citizen, but gave no further details of his location.
The minister said investigators had spoken to Marinova's family and friends and "there is no apparent link to her work".
"Our work is continuing".
"We have collected a lot of evidence which for the time being suggests that the person is guilty".
Viktoria Marinova, 30, is the third journalist to be murdered in the European Union in the past year and the fourth since the start of 2017.
She had recently begun presenting a current affairs talk show that has featured investigative reporting on the alleged embezzlement of funds from the European Union. Last October, Daphne Caruana Galizia, one of Malta's best-known investigative journalists, was killed when a powerful bomb blew up her auto.
A candlelight vigil in memory of murdered Bulgarian journalist Viktoria Marinova in Sofia
Following the murder, Prime Minister Boyko Borisov expressed hope the perpetrator would be found. "None of them true", he told a news conference.
"We, as a country, did not deserve to be smeared like this. while everyone has been working (to solve the crime) not 100, but 1,000 percent".
European Commission President Jean-Claude Juncker praised the Bulgarian authorities' efforts.
"Shocked by the horrendous murder of Victoria Marinova". His repeated attacks on the media's credibility and legitimacy have wide-ranging and risky implications for the safety of journalists and press freedom.
The RSF World Press Freedom Index also states that there is a "growing animosity towards journalists".
Previously she hosted a lifestyle program and was involved with charity work.
On Wednesday, Mr Weber tweeted: "Bulgarian authorities have acted swiftly and effectively".
I will closely follow investigation into horrific murder of investigative journalist Viktoria Marinova in #Bulgaria.
In a statement on their Facebook page, Bivol.bg also called for police protection of Marinova's colleagues.
Thousands of Bulgarians held commemorations on Monday evening with the largest crowds turning out in Ruse where the crime took place, according to Balkan Insight.
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Sister Maryse Alsaint walks alongside a school damaged by a magnitude 5.9 quake the night before in Gros Morne, Haiti, today. Thousands of people along Haiti's north coast have dragged mattresses and chairs outside, fearing new aftershocks.