Kompany led Belgium to victories over Algeria and Russia to qualify for the second round with a game to spare, the only blemish being a nagging groin strain that kept the Manchester City captain sidelined for a few days of training.
Barely half an hour into the last training session on the eve of Thursday's game against South Korea at Sao Paulo, Kompany had to withdraw again and even skipped a planned media appearance.
''He will not be able to play,'' Wilmots said late Wednesday, adding that defender Thomas Vermaelen will be out as well with a hamstring injury.
The two injuries ''are not very serious but we want to keep them fresh and they won't play against South Korea.''
Still, Kompany has a long history of injuries, and his absence in the buildup to the second-round game will further raise uncertainties about Belgium's preparedness for its first knockout game.
Wilmots said Kompany started feeling pain and immediately stopped training, trying to avoid aggravating the injury.
''It hurt a bit and he over-exercised perhaps a bit,'' Wilmots said.
Kompany is expected to have several days of special medical care to get ready for the second round.
For years now, Kompany came to embody the revival of Belgium football, combining skill, brawn and leadership qualities to help push the team into its first World Cup appearance in a dozen years.
He insisted, though, there would still be the backbone of his strongest team to face South Korea. The Asian team still wants to make the most of an outside chance to advance.
''We won't field our B-team against South Korea. I hate that word anyhow,'' he said.
Belgium leads the group with six points, ahead of Algeria with three. Russia and South Korea are left with one each and an outside chance to advance.
Belgium only needs a draw against South Korea to finish top of the group and move into a match against the runner-up in Group G - and likely avoid Germany.
Belgium will know exactly what the scenarios are before Thursday's late kickoff against South Korea.
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- Sports & Recreation
- Vincent Kompany
- Marc Wilmots
- South Korea