The two stars, whose relationship and forthcoming marriage has been closely followed by newspapers and celebrity magazines around the world, had been due to tie the knot on Sunday in Santa Barbra, California.
Affleck and Lopez had claimed they had hired three decoy brides to fool the media, but it was after the location of the wedding was leaked and a police warning that their wedding venue would be easy to gatecrash that they pulled the plug.
In a statement issued to the press, the celebrity couple said: "Due to the excessive media attention surrounding our wedding, we have decided to postpone the date.
"When we found ourselves seriously contemplating hiring three separate decoy brides at three different locations, we realised something was awry.
"We began to feel that the spirit of what should have been the happiest day of our lives could be compromised. We felt what should have been a joyful and sacred day could be spoiled for us, our families and our friends."
The location of the wedding was reported in US Weekly magazine, which said that the vows and reception would occur at Sotto Il Monte, a private mansion in the Montecito, near Santa Barbara.
Those on the guest list were reported to include a host of Hollywood stars including Affleck's friend Matt Damon, as well as Bruce Willis, Matthew Perry, Alec Baldwin, Madonna, Britney Spears, Robin Williams and Colin Farrell.
According to The Sun, a source close to J-Lo said the star was determined to find which of her staff revealed the plans.
"She is absolutely furious. She knows it had to be someone near the top of the pyramid because of the detail -- it was not the kind of stuff a waiter would know. There is a witch-hunt on to find out who it was. Even the guests didn't know until two days ago where the wedding was taking place."
The two had planned a star-studded glittering event, which was set to go down as the biggest Hollywood wedding in recent memory.
The reception itself was to include a transparent dance floor set on the surface of the swimming pool to give the effect that the were waltzing across the surface of the water during the traditional first dance.
Some journalists who have been closely following the couple's wedding preparations speculated that reports of the cancellation could be a bluff to fool the press.
This was dismissed by Dan Klores, Lopez's New York-based spokesman. "I don't see that as even remotely possible," he told Reuters.
Bonnie Fuller, who oversees the Enquirer, Star and Globe tabloids, said: "I think it's a good possibility. I think it's at least 50-50 that the wedding will still take place this weekend but perhaps in a different location."
The cancellation of the wedding follows the drubbing of the stars' first movie together, 'Gigli', which was panned by the critics. The pair were reported to lack on-screen chemistry and the ending had to be reshot.
It bombed at the box office and is now best known for the infamous line uttered by Lopez -- "It's turkey time, gobble gobble gobble". The dialogue is delivered in a key scene where J-Lo is meant to be seducing Affleck for the first time, but its effect was to leave audiences laughing.
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