Todd's son, Jaymes, has been charged with the rape and murder of Dixon whose death sparked discussion over the right for women to feel safe while walking home.
Todd attacked "sneaky" people posting s"**t in public" and shared screenshots of one of his tormentor's posts.
Aimed at Todd, it read: "Hope you're proud… LOL your son is going to get his in prison … he will scream so hard," one user wrote.
Todd posted screenshots from the user's Facebook page in an apparent attempt to shame them.
The posts were deleted shortly after the Herald Sun began making inquiries.
The distraught father ended his missive with the #MeToo hashtag.
He has previously apologised for his son's alleged actions, labelling them "disgusting".
His statements came hours before 10,000 mourners gathered last night in Princes Park - where the comedian's body was found - for a candlelight vigil.
Ms Dixon's death sparked discussion over the right for women to feel safe while walking home.
The 22-year-old's gruesome death stunned the nation and has sparked debate over violence against women.
Hundreds of thousands of posts flooded social media in the wake of her death with the majority expressing grief and solidarity with women.
On Facebook, organisers wrote that the vigil was about a simple message: "We all should be able to walk home, whenever we want, wherever we want, and assume we will make it home safe.
"Our bodies are not there for taking. It is not up to us to keep ourselves safe when we know it's up to men to choose not to inflict violence upon us."
Prime Minister Malcolm Turnbull says Australia must do more to "change the hearts of men" to respect women after comedian Eurydice Dixon's murder.
