The former Manchester City player was stretchered off on 22 minutes after falling awkwardly, with the club later confirming the seriousness of the injury.
"A bittersweet Sunday," club vice-president Adriano Galliani told the club's website.
"De Jong's tendon has snapped and that means the season is over for him.
"It's a big loss for the team and takes the shine off the win."
Holland international De Jong joined the Rossoneri last summer and has made 15 appearances for the club.
Milan ran out 4-2 victors at Torino to record their third successive Serie A win, lifting them to seventh in the league table.