Political analyst and broadcaster Karima Brown has laid charges of incitement of violence and intimidation against a member of the EFF.
This was after she said she received a WhatsApp message from the man, in which he described her as "enemy number one for the EFF".
Brown told News24 that the Sophiatown police station had initially refused to take her complaint, and only did so after "intervention from above".
She says she wants the police to investigate why she is a target.
"After refusing to take my case, and saying I must get a protection order and I wont be helped, I was finally assisted after intervention from above... now I have a case number," Brown said.
Brown is not the first senior journalist to receive threatening messages from individuals linked to the EFF.
Earlier this week, News24 editor-in-chief Adriaan Basson said that he would be opening a criminal case against an EFF supporter who tweeted a call for "action to kill white people like you".
The comment, by one @tsk_tsheko, was made after Basson shared a link to a story about the DA reporting Black First Land First (BLF) leader Andile Mngxitama to the South African Human Rights Commission (SAHRC) and the Equality Court for alleged hate speech comments.
'Open season on journalists'
During a speech in Potchefstroom on December 8, Mngxitama reportedly urged supporters to kill five white people for every one black person that killed in taxi violence.
At the time, EFF spokesperson Mbuyiseni Ndlozi said that @tsk_tsheko did not speak for the EFF.
"The party's official positions are communicated by its leadership," he said, after being asked if the EFF would be condemning such threats by its members.
Basson said it seemed that it was "open season on journalists", adding that it was disturbing and shocking that someone could make such death threats on a public platform like Twitter.
"I am not the first and will not be the last journalist to be threatened on social media platforms. It is time our political leaders take responsibility for the actions of their supporters and condemn this kind of hatred and abuse, particularly in the run-up to next year's elections," Basson said.
In November, the South African National Editors' Forum (Sanef) vowed to take steps, following attacks on journalists by EFF leader Julius Malema and other party members.
This after Malema's comments outside the state capture commission of inquiry in Parktown, Johannesburg, where he identified specific journalists as being "the defence force of President Cyril Ramaphosa and Pravin Gordhan".