The Guinea left back was withdrawn at halftime in the 1-0 defeat to Inter at San Siro.
He is expected to undergo tests when Milan return to training next Monday.
Under-pressure coach Massimiliano Allegri will be hoping Constant is fit for the Serie A encounter with Atalanta after the winter break on January 6 as he battles to save his job.
Milan is already without striker Stephan El Shaarawy because of a foot injury, while Robinho (shoulder) and Ignazio Abate (ankle) are also sidelined together with Valter Birsa (thigh) and Matias Silvestre (calf).
Defeat to Inter left Milan, which has won just four league games this season, 13th in the table, five points above the relegation zone.