The deal is the biggest transaction so far involving a British company to fall victim to the problems in global credit markets which was sparked by poor quality U.S. mortgage loans.
It comes after confectioner Cadbury dropped plans to sell its North American drinks unit and pubs group Mitchells & Butlers put a planned property spin-off on ice.
The Qatari fund, Delta Two, still owns 25 percent of Sainsbury. No one was immediately available to say whether it planned to hold onto the stake, but it said in a statement that it remained supportive of Sainsbury's operational strategy.
"It doesn't look like they're sellers. But it's hard to say what Tchenguiz's plans will be," said Pali International analyst Nick Bubb, referring to property magnate Robert Tchenguiz's approximate 10 percent interest in Sainsbury.
Second Failed Bid
Delta Two's withdrawal marks the second failed bid for Sainsbury in less than seven months. Private equity firm CVC Capital Partners abandoned a takeover attempt in April, following opposition from the Sainsbury family, which owns about 18 percent of the supermarket group.
At 1230 GMT Sainsbury's shares were down 19.3 percent at 447.75 pence, putting Delta Two's stake in Sainsbury into a big loss.
The fund bought most of its stake in April at a price which market sources said was around 575 pence a share. It later bought the rest of its stake at around 595 pence a share.
Seymour Pierce analyst Andrew Wade said although the Sainsbury management team had done "an excellent job starting the recovery and driving sales growth, there is much still left to do" and the share price was substantially overvalued.
Shares in Wm Morrison Supermarkets, which has also been tipped as a possible bid target, fell as much as 7 percent.
Both Sainsbury and Morrison have attracted speculation about possible bids, in part because of their rich property assets.
The Sainsbury board opened its books to Delta Two after it proposed a 600 pence-a-share cash offer, which was above CVC's proposal of 582 pence. However, the Sainsbury family remained lukewarm about selling out at that price.
Delta Two said last month it needed an extra 500 million pounds of funding for its bid from its backer, the Qatar Investment Authority (QIA).
A source close to the matter told Reuters on Sunday there was no certainty the QIA would provide the extra money.
"Since Delta Two's original proposal was submitted to the board of Sainsbury, the required funding and cost of capital has increased significantly, which has adversely affected the investment case," the Qatari fund said in a statement.
"This reflected a combination of factors including the deterioration of credit markets ... and the arrangements for the future funding of the Sainsbury pension schemes necessary to gain the backing of the Sainsbury pension trustees."
Sainsbury said in a separate statement it had a strong future as an independent company and repeated that first-half results, due on Nov. 14, would show sales in line with analysts' expectations for the full year.
"Overall we see about 480 pence as the level the shares will ultimately settle at although it is possible that the shares could overshoot on the downside given the preponderance of arb/event funds on the register ... and the relative dearth of alternative bid scenarios," Cazenove analysts said in a research note, referring in part to short-term traders who were holding Sainsbury shares purely on speculation of a successful deal.