The 28-year-old Holland international was stretchered off just 22 minutes into the Serie A match 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 official 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."
De Jong was a summer signing from Manchester City and has made 15 appearances for the Rossoneri.