A group of computer hackers has tampered with the website of the Sun, owned by News International.
At first, readers were redirected to a hoax story which said Rupert Murdoch had been found dead in his garden.
A group of hackers called Lulz Security, which has previously targeted companies including Sony, said on Twitter it was behind the attack.
Visitors to the Sun website were then redirected to the group's Twitter page, before News International took it down.
News International said it was "aware" of what was happening but made no further comment.
Readers trying to access thesun.co.uk were taken to new-times.co.uk and a story entitled "Media mogul's body discovered".
It suggested that Mr Murdoch had been found after he had "ingested a large quantity of palladium".
After that site stopped working, the Sun's address was re-directing to LulzSec's Twitter account, which claimed to be displaying "hacked internal Sun staff data" in one entry.
In another, the group said: "Arrest us. We dare you. We are the unstoppable hacking generation..."
It is thought the Times website and the News International corporate website were taken down by the company as a precaution on Monday evening.
BBC technology reporter Iain MacKenzie said the attack on the Sun website was in line with LulzSec's "hacktivist" ethos, with the combination of a mischief-making news story, and a target that is seen as being involved in corporate wrongdoing.
He said: "Clearly this is not the most significant development in the scandal currently engulfing News International. But the turning of the hacking tables is, at least, curiously ironic sideshow."
Last month the hacking group announced it was disbanding.
Lulz Security made its announcement through its Twitter account, giving no reason for its decision.
A statement published on a file-sharing website said that its "planned 50-day cruise has expired".
The group leapt to prominence by carrying out attacks on various high-profile companies.
The first came in May 2011 when the hackers targeted Fox.com in retaliation for calling rapper and entertainer Common "vile" on the Fox News channel.
A month later, they turned their attention against Sony, taking data from thousands of people including names, e-mail addresses and dates of birth.
The group has also cyber-attacked broadcaster PBS, the CIA, and the United States Senate.
As a parting shot, it released a selection of documents apparently including confidential material taken from the Arizona police department and US telecoms giant AT&T.