The Irishman, a member of Europe's last two Ryder Cup teams, withdrew from the Irish Open on Thursday and went straight to a hospital, where he had a piece of bone removed from his left knee.
McGinley said he had a piece of bone 'the size and thickness of the tip of a finger' removed.
'I have a 50-50 chance of playing in the (June 1-4) Wales Open but more realistically it will be probably the U.S. Open,' McGinley said Friday.
He said he had known for some time he would need surgery and had started to feel the bone affecting his ability to play shots.
'I have been aware that there was a piece of bone at the back of my left knee but only recently has it floated to the front,' McGinley said. 'That made it easier to remove.'
He said he hoped to be hitting balls within 10 days.
McGinley, who holed the winning putt at The Belfry in 2002, is seventh in the Ryder Cup standings for this year's team but has missed his last four halfway cuts.
The U.S. Open starts June 15.
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