Immediately after fielding J.D. Martinez's ground ball and throwing to first base, Anderson collapsed to the ground in extreme pain.
White Sox training staff helped Anderson off the field and into the clubhouse. He was unable to put any weight on his right leg.
Anderson is also scheduled to have an MRI on Wednesday.
Anderson, who turned 26 on Sunday, is in the midst of a breakout season, slashing .317/.342/.491 with 11 homers, 37 RBIs, and 15 stolen bases.
Tuesday's White Sox-Red Sox game was being played in wet conditions following a pregame downpour that delayed first pitch by 30 minutes. The skies opened up again briefly after the game began.