Beckham sustained the injury without coming into contact with anyone else, limping to the sidelines for treatment in a match Milan went on to win 1-0.
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.
“I cannot enjoy this evening considering this serious injury.
“David understood immediately that he had torn his achilles tendon.”
The England midfielder pulled up sharply with no other players around him and signalled to the bench he had a problem with his left ankle.
A Sky television reporter on the San Siro touchline said Beckham had told the bench “It’s broken, it’s broken” as he came off.
Substitute Clarence Seedorf scored a stoppage-time winner to lift Milan to victory .
The Dutch midfielder entered the game with 11 minutes remaining and knocked in the only goal of the match to pull the Rossoneri to within one point of leaders Inter Milan.
But the result was marred somewhat by Beckham’s injury.
Elsewhere, a Cristiano Lucarelli hat-trick for relegation-threatened Livorno denied Roma the chance to move within four points of Serie A leaders Inter Milan in a 3-3 draw.
Bologna and Sampdoria had to settle for a point each in a 1-1 draw after a dramatic final few minutes at the Stadio Renato Della Ara today.
The game looked destined to end in a stalemate until Daniele Gastaldello grabbed what seemed certain to be the winner for the visitors after 86 minutes.
But Bologna hit back to snatch an equaliser in the second minute of added time when Andrea Raggi fired in from close range.
Siena launched a stunning second-half fightback to recover from 3-0 down and earn a draw as Juventus’ disappointing campaign continued at Stadio Olimpico.
Three goals in the opening 10 minutes from Alessandro Del Piero (2) and Antonio Candreva looked to have secured the points for Alberto Zaccheroni’s fifth-placed side, who had entered the match on the back of three wins from their last four games.
But former Middlesbrough striker Massimo Maccarone got a goal back for the basement battlers just before the interval before two goals from Abdel Ghezzal, the second from the spot, sealed the most unlikely of comebacks.
Elsewhere, Udinese beat Palermo 3- 2 and Parma saw off Atalanta 1- 0 thanks to a Valeri Bojinov’s goal.