Thousands of miners and police clashed at the Yorkshire coking site in 1984.
Campaigners said officers led by South Yorkshire Police were heavy-handed and manufactured statements.
However, Mrs Rudd said she did not believe there was “sufficient basis… to instigate either a statutory inquiry or an independent review”.
Barbara Jackson, secretary of the Orgreave Truth and Justice Campaign, said the announcement had come as a “complete shock and a great disappointment”.
In a written statement, Mrs Rudd said: “Despite the forceful accounts and arguments provided by the campaigners and former miners who were present that day about the effect that these events have had on them, ultimately there were no deaths or wrongful convictions.”
Calls for an Orgreave inquiry escalated following the conclusion of the two-year Hillsborough inquests, which provided a scathing assessment of the under-fire South Yorkshire Police force’s behaviour.
The statement added: “The campaigners say that had the consequences of the events at Orgreave been addressed properly at the time, the tragic events at Hillsborough would never have happened five years later.
“That is not a conclusion which I believe can be reached with any certainty.”
The Battle of Orgreave was the most violent day of the year-long 1984-85 miners’ strike.
Huge lines of police clashed with striking miners as they tried to stop lorries carrying coke to fuel the Scunthorpe steel furnaces.
Violence erupted on both sides and at one stage police horses were sent to charge the crowd up the field as officers followed to make arrests.
The police said they were hit by rocks and bottles and had to react to protect themselves. The miners said they were peacefully protesting when the police charged.
Mrs Rudd acknowledged her decision would be a “significant disappointment” to the Orgreave Truth And Justice Campaign, but said a raft of “very significant changes” to policing since 1984 meant there would be “very few lessons to be learned”.
However, Mr Burnham said: “Given that the IPCC found evidence of perjury and perverting the course of justice, and given that in the last month new evidence has emerged from former police officers who were at Orgreave of orchestrated violence and the mass manufacture of police statements, aren’t we right in concluding that the establishment stitch-up that she has just announced today is nothing more than a naked political act?”
Mrs Rudd said he was “entirely wrong”, accusing him of choosing to “politicise” the decision.
She added: “Just because I have made a decision with which he disagrees, does not mean it is the wrong decision.”
The clash between police and the picket lines during the 1984-85 miners’ strike were the most violent of that whole year.
It marked a step change in police tactics.
Before the “Battle of Orgreave” officers used a defensive strategy.
They held pickets back and they made sure that people could get to work if they wanted to.
But on the fields outside the Orgreave coke works, near Rotherham, new tactics were employed by South Yorkshire Police.
They came on the offensive in riot gear, wielding truncheons and short shields.
It was the first time this approach was used in the UK in such a way.
Mass arrests were made but their cases were thrown out and nobody went to prison.
Could this be why the home secretary decided that this whole issue was not worthy of being re-examined?
Mrs Jackson told the BBC the decision meant there would be “no transparency, no accountability, no truth and no justice”.
“It’s a complete and utter shock to us that we are getting nothing after campaigning for four years,” she said.
“So it’s OK that you get beaten up and seriously injured, but so long as you don’t die the police don’t have to be held accountable.”
She said the campaign groups lawyers would be looking at Mrs Rudd’s decision to see if there was room to mount a legal challenge.
Labour MP for Bolsover, Dennis Skinner, described the announcement as contrary to that of Prime Minister and former Home Secretary Theresa May.
Mrs Rudd, however, said that there had been “no commitment made before, only a willingness to look at the evidence”.
Labour leader Jeremy Corbyn said he was “astonished” and re-committed a Labour government to holding a full inquiry.
He said: “Campaigns for justice never go away.”
Ministers can order public inquiries into events that in the commendably simply legal jargon have caused “public concern”.
On that basis alone, the Orgreave campaigners will say they have been denied justice. In practice, it’s pretty tough to get an inquiry launched.
All recent major inquiries have shared a number of critical factors that boil down to serious allegations of the state failing ordinary people in catastrophic circumstances.
Hillsborough was about the deaths of innocent people.
The troubled Child Sexual Abuse inquiry will look at alleged corruption at the highest levels of government.
The controversial probe into undercover policing, starting next year, came after serious miscarriages of justice and allegations of spying on Stephen Lawrence’s family.
In each case, ministers have accepted lessons still need to be learned and potential wrongs righted.
Any ministerial decision can be challenged – so the question now is whether campaigners think they’ve got a case to take her to court.
South Yorkshire Police and Crime Commissioner Dr Alan Billings said he was “shocked and dismayed” by the decision.
He said: “The government has marched the Campaign for Truth and Justice to the top of the hill, only to march it down again.
“The former miners and the former mining communities in South Yorkshire deserve an explanation as to what happened on that day and where Orgreave fits in the wider story of the miners’ strike.
“I believe the government has shied away from agreeing an inquiry because of those wider issues.”
Hillsborough campaigner Margaret Aspinall said she believed Mrs Rudd should have ordered a public inquiry.
“There’s not going to be what the Hillsborough families had, which was an independent inquiry,” she said
“I think that they should have at least the same. I think it’s a real big, big disappointment.”