He was unchallenged when he suffered the injury and hobbled off before being carried away on a stretcher.
The 34-year-old will fly to Finland on Monday for specialist surgery.
Beckham hoped to be part of England’s World Cup squad but coach Fabio Capello conceded the midfielder’s hopes of making the finals in June appear over.
“We have to wait for the results of the scan but it looks like he is out of the World Cup,” he said in a statement. “I spoke with him after the game on Sunday night to offer my support, as did Franco Baldini.
“David is a great professional and has worked very hard to be ready for the World Cup, so missing it will be a big blow.”
Beckham, who is in his second loan stint with Milan from Los Angeles Galaxy, will almost certainly not be fit for the tournament in South Africa, which starts on 11 June.
He left his hotel in Milan on crutches on Monday morning and is scheduled to arrive in Finland to undergo surgery at the Turku clinic of knee specialist Dr Sakari Orava in the afternoon.
In 2006, Beckham suffered an Achilles injury during England’s World Cup quarter-final defeat by Portugal but recovered in time to play for Real Madrid in their first game of the Spanish season eight weeks later.
However, this time the injury is more serious and Dr Orava gave a bleak outlook of Beckham’s hopes of returning in time for the World Cup, explaining that it would likely to be the middle of June before he can resume training and at least another month before he can return to action.
“To start kicking and playing football will take about three months,” stated Dr Orava. “For maximal performances and maximum kicks and jumps, maybe it takes one month more, three to four months before one is able to do light playing.
“We will have to see whether the tendon is completely severed, partly severed, or something in between. His recovery will depend on what kind of an injury this is, but it will likely take several months before it is completely healed.”
“Today we allow patients to do motion earlier than before. In this case we try to get motion back as soon as possible. The operation takes less than one hour.
“After the first month, there can gradually be more and more motion and muscle contractions and very gradually shifting from light training to harder training in the second month.
“After that, one is usually able to walk and maybe start running lightly after two months if everything goes fine. All this depends on the type of tear.”
Consultant sports physician Dr Tom Crisp felt the injury means Beckham has no chance of playing in the finals in South Africa and he told BBC Radio 5 live: “It’s remotely possible he may be running in three months. The chances of him being fit to play for England are non-existent.”
And AC Milan vice-president Adriano Galliani said the Englishman will be out for “probably five or six months”.
He added: “I saw him and he was suffering. In the dressing room, I took him in my arms and told him that if he wanted, he will be with us next year.”
AC Milan coach Leonardo commented: “Beckham’s injury makes us feel terrible. He understood immediately that he had torn his Achilles tendon.
“He is an extraordinary guy and today’s game proves it yet again. I cannot enjoy this evening considering this serious injury.”
AC Milan team-mate Ignazio Abate revealed the England star was inconsolable.
“He’s not doing well. He was in tears in the dressing room, he wasn’t saying a lot. This has affected us all,” confirmed Abate.
Former Manchester United star Beckham, England’s most capped outfield player with 115 appearances, was bidding to become the first England player to feature in four successive World Cup finals. He shares the record of three with Bobby Moore and Peter Shilton.
And with Tottenham’s Aaron Lennon still suffering from a groin problem, Capello may now turn to both Theo Walcott and Shaun Wright-Phillips to cover the right side of midfield, with James Milner, Joe Cole, Stewart Downing and Adam Johnson also in the reckoning.
Former England defender Martin Keown told BBC Radio 5 live: “Capello’s not stupid, he knew there was a role for Beckham within the squad and this is a massive blow.
“He’s going to be out for six months, he needs to now look at rescuing his career and what’s left of it.
“He’ll be extremely upset, without doubt. I think tonight is a very sad day for the Beckham family.”
Beckham’s loan spells at AC Milan were a deliberate attempt to convince Capello of his worth in an England squad but he was an unused substitute in the recent friendly win over Egypt and was quoted in several Sunday papers as saying he feared for his place.
“Am I banking on going to the World Cup? No, not at all,” he is reported to have said.
“I am not guaranteed to go to South Africa. I have to work hard and hopefully win my place.
“There are a good few months left and plenty of games to play but hopefully I can carry on playing well and get in the squad.”
Sunday’s injury is the latest in a string of heartbreaking World Cup moments for Beckham.
His sending off against Argentina in the second round was widely blamed for costing England their chance of glory in France in 1998.
Four years later he was not fully fit after suffering a broken metatarsal in his foot in the build-up as England went out to 10-man Brazil in the quarter-finals in Japan and South Korea.
In 2006, Beckham limped off midway through the last-eight game against Portugal after sustaining a tear in his right Achilles tendon and a lesion in the ligaments of his left knee.
England went on to lose on penalties and, after the game, Beckham tearfully announced he was relinquishing the captaincy. BBC