The 27-year-old Canadian guard will not play for the World team in next week's All-Star tournament.
Gilgeous-Alexander will miss five games for the reigning champion Thunder before a return is possible.
He has scored 20 or more points in 121 consecutive games. That is five games shy of Wilt Chamberlain's NBA record.
Gilgeous-Alexander is averaging 31.8 points, 6.4 assists and 4.4 rebounds a game for Oklahoma City, which has the NBA's best record at 40-11.
