Margaritis Schinas, spokesman for European Commission president Jean-Claude Juncker, said the commission expected "a swift and thorough investigation" that would "bring those responsible to justice and clarify whether this attack was linked to her work".
Police said a Romanian citizen of Ukrainian origin was being detained for 24 hours while his alibi is checked.
"There is physical evidence to link to the murder", Marinov said Wednesday.
Vigil commemorating Victoria Marinova in Sofia on Monday.
It's not clear if Marinova's murder was related to her journalistic work.
In a statement from the United Nations cultural agency's headquarters in Paris, Azoulay added: "Attacks on journalists erode the fundamental human right to freedom of expression and its corollaries, press freedom and free access to information".
The Commission urged Bulgaria to conduct a rapid investigation and the US embassy said it was shocked by the "horrific murder".
The organization added in its statement that Marinova's last broadcast was an interview with Romanian journalist Attila Biro and a Bulgarian colleague, Dimitar Stoyanov, who were looking into allegations of fraud involving European Union funds.
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Marinova served as a member of the management team of the private television station TVN and hosted an investigative program.
The first episode of her programme, aired on September 30, featured an investigation into fraud allegations against oligarchs and politicians.
Bivol.bg owner Asen Yordanov told AFP that "Viktoria's death, the brutal manner in which she was killed, is an execution".
And even some of Marinova's fellow journalists were not convinced that she was killed because of her reporting.
Instead, the attack seems to have been a spontaneous sexual assault, chief prosecutor Sotir Tsatsarov said, adding that all possibilities were still being considered.
"Investigative journalists are being systematically removed", she said. The journalist said he and his coworkers feared for their safety.