The six-year-old, fourth to Stradivarius in the Gold Cup last month after their pair went off joint-favourites, had been a best-priced 6-1 for the two-mile showpiece.
His absence means the removal of another significant obstacle between Stradivarius successfully defending his Goodwood Cup crown and taking another step towards scooping a £1 million bonus offered by Weatherbys Hamilton.
Vazirabad, the Gold Cup runner-up, has already been ruled out.
Stradivarius had been quoted at a best price of Evens before news of Order Of St George’s defection was announced.
He will land his connections the seven-figure bonus if he wins at Goodwood and then the Lonsdale Cup at York, having already landed the Yorkshire Cup and Gold Cup.
“You won’t see him at Goodwood,” O’Brien said of Order Of St George. “He could appear in the King George if the rain came, but if it didn’t he will be left alone and have a prep for the Irish St Leger. He is in good form at home.”
With the warm spell set to continue for at least another fortnight, the prospects of Order Of St George running at Ascot look slim to zero. He has won the Irish St leger twice before.
Kew Gardens, winner of the Group One Grand Prix de Paris on Saturday evening, is as low as 5-1 for the Goodwood Cup but O’Brien has indicated he will contest the King George.
However, Idaho is set to represent him in the two-mile feature. The brother of Highland Reel, a general 20-1 chance, will step up in trip after flat displays in the Coronation Cup and Hardwicke Stakes.
“The plan is to go to the Goodwood Cup with Idaho,” O’Brien said. “We want to try him over the two miles and see. We always felt he would stay further than a mile and a half.