The singer told The Sun he had performed 10 concerts in "agony" on his European tour before he called in doctors.
"I was a ticking time bomb. I guess I could have died at any time," he said.
According to his website, he is on a course of "intensive antibiotics" and is expected to undergo surgery "in the coming weeks".
Sir Elton has had to postpone a series of summer festival dates including shows in Italy, Germany and London's Hyde Park this week.
A spokesman said the diagnosis had been made "following a number of exploratory scans and blood tests with his medical team in the UK".
He confirmed the singer would not return to touring until he had fully recovered from both the planned surgery and any damage caused by the appendix abscess.
"Elton is incredibly disappointed to postpone these tour dates," he said.
"To know that he made such super-human efforts and continued to perform to thousands through his illness only confirms his dedication to his European fans.
"He is eager to be back on top form and return to play the remaining shows starting in early September 2013."
Sir Elton had been due to perform at the Collisioni festival in Italy on Tuesday, with further shows in Germany on Thursday and a headline gig at London's Hyde Park on Friday.
British Summer Time festival organisers AEG Live said the Hyde Park show would still go ahead with Elvis Costello and former Kinks frontman Ray Davies on the bill, with existing ticket holders receiving a full refund.
Other July dates now scrapped include festivals in Spain, France and Monaco.
Sir Elton is due back in the UK in September, performing at the First Direct Arena in Leeds and at Bestival before heading back to Las Vegas for a month-long residency at The Colosseum.

Abigail is the first storm to be given a name by the Met Office who keep track of our weather.
The storm will hit Northern Ireland with strong winds on Thursday afternoon, and move towards the west coast of Scotland and northern England on Friday.
As if one storm wasn't enough, the UK will also be battered by ex-hurricane Kate, which is the end of a hurricane from the Atlantic Ocean. Kate will bring lots more rain for Scotland, Wales and northern parts of England.
Weather forecasters have told people to make sure they are prepared for strong winds, especially in Scotland. Several schools have already shut in the Western Isles in Scotland because of the bad weather.

An "in-depth investigation" will look into claims made by Veracruz governor Miguel Angel Yunes Linares on Monday, the Ministry of Health said.
He alleged fake medicine had been bought and used in state hospitals under his predecessor Javier Duarte.
Mr Duarte has been on the run from the authorities since October.
The former governor, who was elected in 2010,  has not been seen since a week after he stepped down amid allegations of corruption.
He has been charged with organised crime and money laundering, but there are calls for the Attorney General's office to file criminal charges relating to the latest accusations.
On Monday, Mr Yunes Linares told a press conference that an investigation into malfeasance and corruption under Mr Duarte had uncovered medical fraud.
`We have tests on a medication given to children, a paediatric chemotherapy that wasn't really a medication, it was an inert substance, practically distilled water,'' he said.
"This really seems to us a brutal crime, an attempt against the lives of the children. We're finishing our analysis and, at the appropriate time, we'll be filing legal complaints."
Mr Yunes Linares also alleged there had been inadequate tests for HIV detection and the existence of outdated medicines.
The allegations have shocked Mexico.
"It is absolutely inhuman, criminal," Senator Roberto Gil Zuart said, according to Mexican news site Quadratin.
Mexico's Secretary of Health JosÃ© Narro Robles has promised to act on "the persons or companies involved" if irregularities or responsibility is found, the ministry said in a statement on Wednesday.
Sir Elton John has said he is "lucky to be alive" after being diagnosed with appendicitis.
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Much of the UK will be hit by Storm Abigail on Thursday, bringing lots of rain and strong winds.
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Mexican authorities are to investigate allegations children battling cancer were given "distilled water" instead of chemotherapy.