Jagendra Singh died on Monday, a week after he was allegedly set on fire by a group of men in Uttar Pradesh state.
The attack happened after he published an article and posted allegations of corruption on Facebook against ruling party politician Ram Murti Singh Verma.
Police have registered a complaint of murder and criminal conspiracy against Mr Verma, who denies the charges.
Jagendra Singh's family has alleged that Mr Verma and a group of policemen assaulted the 42-year-old journalist at his home and then doused him with petrol and set him on fire.
A local police official claimed that Mr Singh had "committed suicide" when the police arrived at his house in Shahjahanpur district to "arrest him" in connection with a case.
Amnesty International has urged the government of Uttar Pradesh to launch an independent investigation into the incident.
"This horrific attack highlights the dangers that journalists can face in doing their jobs," Shemeer Babu of Amnesty International India said in a statement.
Although police have opened a case against Mr Verma and five others in connection with the incident, no arrests have been made yet.
"We have booked the minister for murder and criminal conspiracy and the investigations are on," Vijay Singh Meena, a senior state police official, told AFP news agency.
The Press Council of India (PCI) also called for a special investigation into the incident, saying the incident was "an attack on freedom of press".
Journalists often face harassment and intimidation by police, politicians and bureaucrats in India.
The country ranked 136 out of 180 nations in the 2015 World Press Freedom Index, according to Paris-based Reporters without Borders.
Rights group Amnesty International has called for an inquiry into the alleged killing of a journalist in India.