The 28-year-old Holland international lasted just 22 minutes of the Rossoneri's 4-2 victory at Torino on Sunday before falling awkwardly and having to leave the pitch on a stretcher.
A statement released on acmilan.com today read: "AC Milan can confirm that Nigel de Jong underwent surgery at Benalmandena near Malaga today.
"The player ruptured the Achilles tendon in his left leg during Torino-Milan.
"The surgery has been a complete success. The recovery time will be around six months, barring any complications."
De Jong joined Milan from Manchester City this summer and had made 15 appearances before injury brought his season to a premature conclusion.
Club vice-president Adriano Galliani told acmilan.com yesterday: "A bittersweet Sunday.
"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."