Young suffered the injury in a 117-112 victory at Brooklyn on Wednesday and an MRI exam on Friday confirmed the extent of the injury and that he suffered no major structural damage.
Four-time NBA All-Star Young has begun rehabilitation and will be re-evaluated in about four weeks, the team said in a statement.
The 27-year-old American, last season's NBA assists leader, has 17.8 points and 7.8 assists a game this season for the Hawks (3-3).
Young looks to miss 14 games for Atlanta before a possible return on November 30 at Philadelphia.