The move came as the House of Commons prepared to vote for a motion supported by all major party leaders calling on Mr Murdoch to scrap the bid.
It follows a scandal over phone hacking at News Corp's UK newspaper group.
News Corp deputy chairman Chase Carey said the bid had become "too difficult to progress in this climate".
The scandal has already led to the closure of the UK's biggest-selling newspaper, the News of the World.
On Friday, Prime Minister David Cameron announced details of a public inquiry into phone hacking and media regulation.
Market reaction"We believed that the proposed acquisition of BSkyB by News Corporation would benefit both companies, but it has become clear that it is too difficult to progress in this climate," said News Corp deputy chairman and president Chase Carey in a statement.
"News Corporation remains a committed long-term shareholder in BSkyB. We are proud of the success it has achieved and our contribution to it."
BSkyB's share price briefly dropped following the announcement, taking it down 4% for the day, before recovering to close 2% up.
The company's share price has fallen some 20% since peaking at 850p earlier this month, and is now trading at a level not seen since News Corp first announced its bid plans in June last year.Following News Corp's announcement, BSkyB chief executive Jeremy Darroch said: "We remain very confident in the broadly based growth opportunity for BSkyB."
'Huge humiliation'A spokesman for Mr Cameron welcomed the news: "As the prime minister has said, the business should focus on clearing up the mess and getting its own house in order."
The Labour leader, Ed Miliband, called it "a victory for people up and down this country who have been appalled by the revelations of the phone hacking scandal and the failure of News International to take responsibility".
Continue reading the main story Liberal Democrat deputy leader Simon Hughes said that "the sun is now setting on the Murdoch empire".The BBC's business editor Robert Peston said: "It's a huge humiliation. This was [News Corp's] biggest investment plan of the moment. It was one of the biggest investments they've ever wanted to make.
"It is an extraordinary reversal of corporate fortune... And questions will now be asked whether this is the full extent of the damage to the empire."
News Corp already owns 39% of BSkyB, but may be compelled to give up even this minority stake if it is deemed not to be a "fit and proper" by regulator Ofcom following the conclusion of current police investigations.
Robert Peston added there had been "a lot of speculation" that Mr Murdoch might now want to sell his UK newspapers, but the current state of the industry made them less attractive to potential buyers.
"The question is, who is going to pay him the price that they are worth? He will not want to sell those papers at a loss."
Business Secretary Vince Cable said it would be "very difficult" to imagine the BSkyB bid being resurrected at a later date.
Mr Cable, who was secretly recorded last year saying he had "declared war" on Rupert Murdoch, had been in charge of overseeing the bid, but was replaced by Culture Secretary Jeremy Hunt.
Public inquiryMr Cameron has asked Lord Justice Leveson to oversee a public inquiry into the News of the World scandal and media regulation.
Continue reading the main story Culture, practices and ethics of the pressTheir relationship with the policeFailure of current regulationContacts made and discussions between national newspapers and politiciansWhy previous warnings about press misconduct were not heededIssue of cross-media ownershipIn a statement to the Commons, he said the inquiry would begin as "quickly as possible" and would be in two parts - an investigation of wrongdoing in the press and the police, and a review of regulation in the press.The judge will have powers to call media proprietors, editors and politicians to give evidence under oath, the PM said.
Mr Cameron said those who sanctioned wrongdoing should have no further role in running a media company in the UK.
He said Lord Justice Leveson, assisted by a panel of senior independent figures, would make recommendations for a better way of regulating the press which "supports their freedom, plurality and independence from government but which also demands the highest ethical and professional standards".
He will also make recommendations about the future conduct of relations between politicians and the press.
Mr Cameron told MPs he would require all ministers and civil servants to record meetings with senior editors and media executives to help make the UK government "one of the most open in the world".
Mr Miliband welcomed the proposal, arguing it must be imposed retrospectively, so that he and Mr Cameron publish all details of meetings with media executives dating back to the last general election.
Continue reading the main storyLord Justice (Sir Brian) Leveson became a barrister in 1970 and a QC 16 years later.
The 62-year-old was made a High Court judge in 2000 and appointed to the Court of Appeal in 2006. He was senior presiding judge there from 2006 to 2009 and now, as chairman of the Sentencing Council, is responsible for criminal sentencing policy in England and Wales.
Lord Justice Leveson is well known for being the barrister who led the prosecution case against serial killer Rose West, who was jailed in 1995 for the murder of 10 women and girls.
He was also the judge during the 2006 trial over the murder of 10-year-old London schoolboy Damilola Taylor.
The prime minister was previously criticised for meeting Rupert Murdoch, head of News Corporation, in Downing Street soon after the election, because Mr Murdoch did not walk through the front door.Newspapers which did not support the government ran stories of "secret meetings".
Earlier at prime minister's questions, Mr Cameron said a "firestorm" was engulfing parts of the media and police, and those who had committed offences must be prosecuted.
Mr Miliband said it was an insult to the family of murdered schoolgirl Milly Dowler, whose phone was allegedly hacked, that Rebekah Brooks was still News International's chief executive.
Mr Cameron responded: "She was right to resign, that resignation should have been accepted. There needs to be root and branch change at this entire organisation.
"What has happened at this company is disgraceful - it's got to be addressed at every level."
In other developments:
Continue reading the main storyThe political classes will feel tonight that they have stood up to Rupert Murdoch and won - for now”End Quote
Nick Robinson BBC Political Editor Meanwhile, Labour's communications chief Tom Baldwin is facing renewed questions over claims he handled private information which was gained illegally during his years at the Times newspaper, another News International publication.The former Conservative deputy chairman Lord Ashcroft makes the allegations in a blog posting on ConservativeHome, which he owns. Mr Baldwin has not responded to the claims.
News Corp already owns 39% of BSkyB The government has said it is "minded to accept" News Corp's assurances about the spin-off of Sky News, but is to consult on some fresh conditions.
Torin Douglas BBC media correspondent