Prosecutors said the 30-year-old had been raped, beaten and suffocated. Marinova's body was found in a park near the Danube river in Ruse on Saturday (local time).
"There is no democracy without a free press ... We expect a swift and thorough investigation to bring those responsible to justice," the European Commission, the European Union's executive said in a tweet.
Bulgaria ranked 111 out of 180 countries in the Reporters Without Borders world press freedom index this year, lower than any other EU member.
While there has been no link established to her work so far, the killing has angered and upset many in a country where people are frustrated with rampant corruption and an inefficient and graft-prone judiciary, for which Sofia has been repeatedly rapped by the European Commission.
On her last aired TV show, on September 30, Marinova introduced two journalists who were investigating alleged corruption involving EU funds. She said the regional current affairs show, "Detector", would do similar investigations.
Chief Prosecutor Sotir Tsatsarov said a bank transfer of 14 million euros ($US16.06 million) had been frozen as part of a pre-trial investigation into issues raised by the investigative journalists on the show but declined to give further details.
"There is no way that I can believe that this killing is random, after it happened just few days after the show that featured such massive misuse of funds. I am glad so many people are here," said Stoyka Panagonova, a mother of three, at the vigil in Ruse.
The European anti-fraud office OLAF declined to comment on the killing. But its press office said it was "aware of allegations concerning possible misuse of EU funds in Bulgaria that have been brought to light by journalists in recent weeks".
Marinova's appearance on "Detector" was the first time she had anchored the show on Ruse-based TV station TVN - a popular channel in northeastern Bulgaria. Previously, she was best known for presenting a regional lifestyle show and was not a household name nationally.
Interior Minister Mladen Marinov has said that there was no evidence to suggest a link to Marinova's work as journalist so far - something echoed by police and prosecutors.
"We are working on all possible motives and we do not exclude any," Marinov told reporters in Ruse, Bulgaria's main Danube river port city.
He said no match had been found so far for DNA collected from the crime scene, which was close to a psychiatric clinic.
Police and prosecutors said they were working on three possible motives - whether Marinova was a victim of a random attack by a person with a mental disorder, a planned attack or whether the crime was linked to her personal life.
Marinova would be the third journalist murdered in the European Union over the past 12 months.
Daphne Caruana Galizia, Malta's best-known investigative reporter, was killed when a bomb blew up her car in October last year and Slovak journalist Jan Kuciak was shot dead in February.
Hundreds of people flocked to Ruse's main square to put flowers in front of a picture of Marinova, with some in the crowds urging the authorities not to play down the possibility her work was a reason for the killing.
"I strongly hope that the truth will soon be uncovered, her perpetrator or perpetrators found and justly punished," Teodora Shopova said after lighting a candle at the vigil.
Vigils for Marinova, mother of a 7-year-old daughter, were also held in downtown Sofia as well as several other cities, with many demanding justice and an independent, even international, investigation.
The TVN channel expressed shock over the killing of its colleague and board member, but declined to comment further.
