The Rossoneri wing-back angrily left the field of play during a pre-season meeting with Sassuolo following a tirade of insults from the stands
Sassuolo recorded a 2-1 victory to win the friendly tournament, but much of the post-match talk was about the incident involving Constant rather than Milan's surprising defeat.
The Guinea international was hit with a torrent of insults from supporters after 34 minutes of play and fired the ball into the stands before angrily storming off, with Milan skipper Daniele Bonera attempting to calm down his team-mate.
Referee Andrea Gervasoni consequently ordered the stadium announcer to send out a message warning the crowd that the game would be suspended if any other incidents occurred.
Tuesday's event comes after a number of racist incidents to affect Milan during the 2012-13 campaign. Kevin-Prince Boateng stormed off in a friendly against Pro Patria earlier this year before Inter fans levelled abuse at former striker Mario Balotelli when the sides met in Serie A.