Kompany misses training with groin strain
Wilmots' side got their FIFA World Cup campaign off to a winning start on Tuesday as they came from behind to beat Algeria 2-1.
However, Belgium's captain would now appear to be a doubt for Sunday's match against Russia at the Maracana in Rio de Janeiro.
Wilmots said on his official Twitter account: "Vincent Kompany was not in training today. He has a light strain to the groin.
"He has been working individually with the medical staff."
The Manchester City star completed the entire 90 minutes against Algeria, alongside Daniel van Buyten in the heart of defence.