Police and prosecutors have been investigating Marinova's murder, which happened after she hosted a programme about two Romanian and Bulgarian investigative journalists from Rise Romania and Bivol.bg who were detained while reporting on an alleged fraud case involving European funds.
On Tuesday, police in Ruse arrested a Romanian citizen in connection with the murder, but later released him without charge due to a lack of concrete evidence.
The man, who wasn't identified, would be freed "very shortly", said Teodor Atanassov, chief police officer of the northern town of Ruse.
"Her death was caused by blows to the head and suffocation, and her mobile phone, vehicle keys, glasses and some of her clothing were missing", said Ruse regional prosecutor Georgy Georgiev.
The minister said investigators had spoken to Marinova's family and friends and "there is no apparent link to her work".
Marinova was a director of TVN, a TV station in Ruse, and a TV presenter for two investigative programs.
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Officials and the police said there was no evidence to suggest Ms Marinova's murder was related to her work and there was no information to say she had been threatened.
A reporter from TVN told AFP, "We are in shock".
The murder case has shocked fellow journalists and sparked global condemnation. "In no way, under any form, never have we received any threats - aimed at her or the television".
While she did not appear to have been closely involved in the fraud investigation, her show touched on a sensitive subject in Bulgaria, where corruption is endemic.
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, vehicle arson and bombs targeting investigative reporters".
"Shocked by [the] horrific murder of investigative journalists Victoria Marinova in #Bulgaria", read a tweet from the Organization for Security and Co-operation in Europe. She is the third journalist to have been murdered in the European Union in the past year.
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).