The 34-year-old, who was hoping to play in his fourth World Cup, was injured while playing for AC Milan against Chievo and will now go to Finland Monday for surgery.
"A rupture of the Achilles tendon is suspected," AC Milan said in a statement.
Milan vice-president Adriano Galliani said England's most-capped outfield player, with 11 caps, will be out for "probably five or six months", but also offered him hope for the future.
"I saw him and he was suffering," Galliani said. "In the dressing room, I took him in my arms and told him that if he wanted, he will be with us next year."
Milan coach Leonardo said: "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."
Ignazio Abate, his Milan teammate, said Beckham was struggling to cope with the news.
"He's not doing well," Abate said. "He was in tears in the dressing room, he wasn't saying a lot. This has affected us all."
