Bayern captain Van Bommel aggravated his injury during Netherlands' 1-0 win over Moldova in a Euro 2012 qualifier last week and went on to play for much of the game in their 4-1 win against Sweden on Tuesday.
He will now miss Bayern's league match against Hanover 96 and will not be available for their Champions League home game against Romania's Cluj next week, the club said.
"Unfortunately what we feared before the match between Netherlands and Sweden has actually happened," said club chief Karl-Heinz Rummenigge in a statement.
"It would have been responsible if Mark van Bommel had returned to Munich yesterday for medical checks," he said.
"Instead it became clear once more that a federation thinks only of its own interest and even risks the health of the players," Rummenigge said, adding the club would inform European football's governing body UEFA of the incident and reserve its rights for possible legal action.
The German champions are already locked in a dispute with the Dutch federation over winger Arjen Robben who aggravated a muscle injury playing in this year's World Cup in South Africa.
Bayern have demanded compensation for the duration of Robben's absence. Robben, who helped Bayern to the domestic championship and Cup double and the Champions League final last season, is not expected to return until early next year.
