The Guinea left-back was withdrawn at half-time with an ankle problem in the 1-0 defeat to Inter and the Rossoneri will find out next week the extent of the damage
The Guinea left-back was withdrawn at half-time in the 1-0 defeat to Inter at San Siro.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 are already without striker Stephan El Shaarawy due to 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, who have won just four league games this season, 13th in the table, five points above the relegation zone.