Kompany limped out of City's 3-1 Premier League win over Everton on Saturday and on Monday the club confirmed the injury was a thigh problem.
The defender has been due to play for Belgium in Friday's crucial World Cup qualifier away to Croatia - a point will see them reach next summer's finals in Brazil - but Belgian officials ruled him out of that clash and next Tuesday's meeting with Wales on Monday evening.
It was they who said Kompany would be out for up to four weeks.
Were Kompany to miss the next four weeks, he would miss key games for City, including a Champions League trip to CSKA Moscow and a Premier League showdown at title rivals Chelsea.
Source: Manchester City MAD