Beckham sustained the injury without coming into contact with anyone else, limping to the sidelines for treatment in the dying moments of AC Milan's 1-0 victory over Chievo before leaving the San Siro on crutches.
Milan coach Leonardo said after the game: "Beckham's injury makes us feel terrible. He is an extraordinary guy and today's game proves it yet again.
"David understood immediately that he had torn his Achilles tendon. When the tendon breaks, everything comes away and the muscle starts to rise. I felt great pity for him. This injury has been a heavy blow for him and for us. Unfortunately the party is ruined."
Initial reports suggested the England midfielder would be out for around three months but the club's physio has since revealed he expects the player to spend five to eight months on the sidelines.
Beckham has already spoken to Fabio Capello and his assistant, Franco Baldini, over the news that he will miss out on the chance to play in his fourth World Cup.
AC Milan midfielder Ignazio Abate said: "Beckham is not well. To see him suffer like that has really touched us."
Clarence Seedorf found it hard to celebrate his last-gasp match-winning goal - which puts Milan just one point behind Inter in Serie A - knowing that Beckham could have a long injury lay-off.
"It's always ugly to be out because of an injury, but it will mean that we will all need to give everything we have even for those who will not be with us," he said. "They deserve that for what they have done so far this season."
Milan have revealed that Beckham is set to fly to Finland on Monday for an operation on the problem. His parent club, LA Galaxy, are understood to be awaiting further news on the incident before issuing a statement on his future.
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