He's missed the last few days of training already, and Brazil are taking no chances as they prepare and are shutting him down before the competition even begins. The injury doesn't appear to be too serious, but Brazil's first game is on June 4, there's no time to waste. However, with Neymar already scheduled to miss the tournament in order to play in the Rio Olympics, Costa is a big blow to their chances of winning.
The positive news here is that Costa will get an extended vacation and should be ready for the first day of Bayern training under new head coach Carlo Ancelotti in July.
Brazil kicks of the tournament with a match against Ecuador on June 4 at the Rose Bowl in Pasadena. Their other two matches are against Haiti on June 8 in Orlando, and Peru on June 12 in Foxborough.