It is expected to be three months at the very earliest before he can run, and double that before he has a chance of playing again.
Fabio Capello: "We have to wait for the results of the scan, but it looks like he is out of the World Cup.
"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.
"'I am very sad for David that he has suffered this injury.''
Beckham spoke of his fear of missing the World Cup in the wake of Milan's hammering by Manchester United last week, and there was some doubt he would have made Capello's final 23.
Aaron Lennon, Theo Walcott and Shaun Wright-Phillips are all under consideration, but Milner can play full-back, central midfield and on either wing, and is thought to be the favourite.