Beckham was getting ready to kick a ball unchallenged when he suddenly pulled up and signalled to the bench despite second-placed Milan having used all their substitutes.
Beckham told the San Siro bench "It's broken, it's broken" as he came off. Team-mates said he was in tears in the dressing room.
"When the Achilles tendon goes you feel it straight away," Milan coach Leonardo told reporters after his side moved one point behind stuttering leaders Inter Milan with 10 games left.
"The injury to David is upsetting. This injury lets me enjoy the win less."
Milan officials told reporters he would fly to Finland as soon as possible to be operated on by a specialist.
The 34-year-old, on loan at Milan from Los Angeles Galaxy chiefly to try to safeguard his England squad place for the World Cup, will now almost certainly not be fit for the tournament in South Africa which starts on June 11.
Television analysts said Achilles injuries can take up to three months to heal, sometimes as much as five months.
England are well-covered on the right wing with Theo Walcott, Shaun Wright-Phillips and James Milner among the players able to play there. Tottenham Hotspur's Aaron Lennon is currently injured.
Beckham, a former captain who played at the 1998, 2002 and 2006 World Cups, is England's most capped outfield player with 115 appearances.
He suffered a broken metatarsal in his foot in 2002 and was not fully fit for the 2002 World Cup, when England went out in the quarter-finals.
Milan, bidding for their first scudetto since 2004, will also miss his crossing ability although he has been far less effective in this loan spell compared to his first stint at the San Siro last year.
A dejected-looking Beckham, who left the San Siro on crutches to applause and kisses from club officials, was due to return to Galaxy after the World Cup.
He gave no comment to reporters.
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