The woman was a student of Fakir Mohan (Autonomous) College in Balasore.
The victim's brother alleged some people were trying to exploit the tragedy for political gains and named four people in connection with the defamatory content in his complaint.
The Odisha Police have launched an investigation into the allegations of cyber harassment.
"On social media, people are making derogatory remarks and posting filthy posts and comments. In our bad times, we are being made to bear this unnecessary trolling and abuse online," he said.
"I have sought the help of police and administration and filed a first information report (FIR) against some people," he said. He added the family needs proper protection and free and fair investigation.
"We will all die by suicide if we don't get justice," he said.
The police are verifying the social media accounts of people named in the complaint filed by the victim's brother.
The woman, a second-year integrated BEd student, had set herself on fire on July 12 after allegedly being denied justice in the sexual harassment case filed by her against the professor, Samira Kumar Sahoo.
The woman suffered 95 per cent burn injuries. She died on Monday night after battling for her life for almost 60 hours at AIIMS Bhubaneswar.
Two people including the accused professor and the college principal, Dilip Ghose, have been arrested on charges of abetment to suicide and sexual harassment.
(With inputs from Dev Kumar)
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